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Lattice Surgery for Dummies

Published 19 Apr 2024 in quant-ph | (2404.13202v2)

Abstract: Quantum error correction (QEC) plays a crucial role in correcting noise and paving the way for fault-tolerant quantum computing. This field has seen significant advancements, with new quantum error correction codes emerging regularly to address errors effectively. Among these, topological codes, particularly surface codes, stand out for their low error thresholds and feasibility for implementation in large-scale quantum computers. However, these codes are restricted to encoding a single qubit. Lattice surgery is crucial for enabling interactions among multiple encoded qubits or between the lattices of a surface code, ensuring that its sophisticated error-correcting features are maintained without significantly increasing the operational overhead. Lattice surgery is pivotal for scaling QECCs across more extensive quantum systems. Despite its critical importance, comprehending lattice surgery is challenging due to its inherent complexity, demanding a deep understanding of intricate quantum physics and mathematical concepts. This paper endeavors to demystify lattice surgery, making it accessible to those without a profound background in quantum physics or mathematics. This work explores surface codes, introduces the basics of lattice surgery, and demonstrates its application in building quantum gates and emulating multi-qubit circuits.

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References (44)
  1. M. Reiher, N. Wiebe, K. M. Svore, D. Wecker, and M. Troyer, “Elucidating reaction mechanisms on quantum computers,” Proceedings of the national academy of sciences, vol. 114, no. 29, pp. 7555–7560, 2017.
  2. R. Orús, S. Mugel, and E. Lizaso, “Quantum computing for finance: Overview and prospects,” Reviews in Physics, vol. 4, p. 100028, 2019.
  3. M. Schuld, I. Sinayskiy, and F. Petruccione, “An introduction to quantum machine learning,” Contemporary Physics, vol. 56, no. 2, pp. 172–185, 2015.
  4. P. Gachnang, J. Ehrenthal, T. Hanne, and R. Dornberger, “Quantum computing in supply chain management state of the art and research directions,” Asian Journal of Logistics Management, vol. 1, no. 1, pp. 57–73, 2022.
  5. A. Ajagekar and F. You, “Quantum computing for energy systems optimization: Challenges and opportunities,” Energy, vol. 179, pp. 76–89, 2019.
  6. A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, “Introduction to quantum noise, measurement, and amplification,” Reviews of Modern Physics, vol. 82, no. 2, p. 1155, 2010.
  7. G. Mouloudakis and P. Lambropoulos, “Entanglement instability in the interaction of two qubits with a common non-markovian environment,” Quantum Information Processing, vol. 20, pp. 1–15, 2021.
  8. S. J. Devitt, W. J. Munro, and K. Nemoto, “Quantum error correction for beginners,” Reports on Progress in Physics, vol. 76, no. 7, p. 076001, 2013.
  9. R. W. Hamming, “Error detecting and error correcting codes,” The Bell system technical journal, vol. 29, no. 2, pp. 147–160, 1950.
  10. W. K. Wootters and W. H. Zurek, “The no-cloning theorem,” Physics Today, vol. 62, no. 2, pp. 76–77, 2009.
  11. N. Sundaresan, T. J. Yoder, Y. Kim, M. Li, E. H. Chen, G. Harper, T. Thorbeck, A. W. Cross, A. D. Córcoles, and M. Takita, “Matching and maximum likelihood decoding of a multi-round subsystem quantum error correction experiment,” arXiv preprint arXiv:2203.07205, 2022.
  12. M. Abobeih, Y. Wang, J. Randall, S. Loenen, C. Bradley, M. Markham, D. Twitchen, B. Terhal, and T. Taminiau, “Fault-tolerant operation of a logical qubit in a diamond quantum processor,” Nature, vol. 606, no. 7916, pp. 884–889, 2022.
  13. D. Bacon, “Operator quantum error-correcting subsystems for self-correcting quantum memories,” Physical Review A, vol. 73, no. 1, p. 012340, 2006.
  14. A. Y. Kitaev, “Quantum computations: algorithms and error correction,” Russian Mathematical Surveys, vol. 52, no. 6, p. 1191, 1997.
  15. S. Krinner, N. Lacroix, A. Remm, A. Di Paolo, E. Genois, C. Leroux, C. Hellings, S. Lazar, F. Swiadek, J. Herrmann et al., “Realizing repeated quantum error correction in a distance-three surface code,” Nature, vol. 605, no. 7911, pp. 669–674, 2022.
  16. H. Bombin and M. A. Martin-Delgado, “Topological quantum distillation,” Physical review letters, vol. 97, no. 18, p. 180501, 2006.
  17. D. Horsman, A. G. Fowler, S. Devitt, and R. Van Meter, “Surface code quantum computing by lattice surgery,” New Journal of Physics, vol. 14, no. 12, p. 123011, 2012.
  18. A. J. Landahl and C. Ryan-Anderson, “Quantum computing by color-code lattice surgery,” arXiv preprint arXiv:1407.5103, 2014.
  19. A. Cowtan, “Qudit lattice surgery,” arXiv preprint arXiv:2204.13228, 2022.
  20. A. Erhard, H. Poulsen Nautrup, M. Meth, L. Postler, R. Stricker, M. Stadler, V. Negnevitsky, M. Ringbauer, P. Schindler, H. J. Briegel et al., “Entangling logical qubits with lattice surgery,” Nature, vol. 589, no. 7841, pp. 220–224, 2021.
  21. A. G. Fowler and C. Gidney, “Low overhead quantum computation using lattice surgery,” arXiv preprint arXiv:1808.06709, 2018.
  22. D. Litinski, “A game of surface codes: Large-scale quantum computing with lattice surgery,” Quantum, vol. 3, p. 128, 2019.
  23. D. Herr, A. Paler, S. J. Devitt, and F. Nori, “Lattice surgery on the raussendorf lattice,” Quantum Science and Technology, vol. 3, no. 3, p. 035011, 2018.
  24. C. Chamberland and E. T. Campbell, “Circuit-level protocol and analysis for twist-based lattice surgery,” Physical Review Research, vol. 4, no. 2, p. 023090, 2022.
  25. ——, “Universal quantum computing with twist-free and temporally encoded lattice surgery,” PRX Quantum, vol. 3, no. 1, p. 010331, 2022.
  26. D. Herr, F. Nori, and S. J. Devitt, “Optimization of lattice surgery is np-hard,” Npj quantum information, vol. 3, no. 1, p. 35, 2017.
  27. N. de Beaudrap and D. Horsman, “The zx calculus is a language for surface code lattice surgery,” Quantum, vol. 4, p. 218, 2020.
  28. C. Vuillot, L. Lao, B. Criger, C. G. Almudéver, K. Bertels, and B. M. Terhal, “Code deformation and lattice surgery are gauge fixing,” New Journal of Physics, vol. 21, no. 3, p. 033028, 2019.
  29. A. Chatterjee, K. Phalak, and S. Ghosh, “Quantum error correction for dummies,” in 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), vol. 1.   IEEE, 2023, pp. 70–81.
  30. J. Chiaverini, D. Leibfried, T. Schaetz, M. D. Barrett, R. Blakestad, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer et al., “Realization of quantum error correction,” Nature, vol. 432, no. 7017, pp. 602–605, 2004.
  31. E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, “Topological quantum memory,” Journal of Mathematical Physics, vol. 43, no. 9, pp. 4452–4505, 2002.
  32. A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, “Surface codes: Towards practical large-scale quantum computation,” Physical Review A, vol. 86, no. 3, p. 032324, 2012.
  33. V. Kolmogorov, “Blossom v: a new implementation of a minimum cost perfect matching algorithm,” Mathematical Programming Computation, vol. 1, pp. 43–67, 2009.
  34. Y. Tomita and K. M. Svore, “Low-distance surface codes under realistic quantum noise,” Physical Review A, vol. 90, no. 6, p. 062320, 2014.
  35. M. H. Freedman and D. A. Meyer, “Projective plane and planar quantum codes,” Foundations of Computational Mathematics, vol. 1, pp. 325–332, 2001.
  36. S. B. Bravyi and A. Y. Kitaev, “Quantum codes on a lattice with boundary,” arXiv preprint quant-ph/9811052, 1998.
  37. N. C. Jones, R. Van Meter, A. G. Fowler, P. L. McMahon, J. Kim, T. D. Ladd, and Y. Yamamoto, “A layered architecture for quantum computing using quantum dots,” arXiv preprint arXiv:1010.5022, 2010.
  38. D. A. Herrera-Martí, A. G. Fowler, D. Jennings, and T. Rudolph, “Photonic implementation for the topological cluster-state quantum computer,” Physical Review A, vol. 82, no. 3, p. 032332, 2010.
  39. D. P. DiVincenzo, “Fault-tolerant architectures for superconducting qubits,” Physica Scripta, vol. 2009, no. T137, p. 014020, 2009.
  40. P. Groszkowski, A. G. Fowler, F. Motzoi, and F. K. Wilhelm, “Tunable coupling between three qubits as a building block for a superconducting quantum computer,” Physical Review B, vol. 84, no. 14, p. 144516, 2011.
  41. J. Kruse, C. Gierl, M. Schlosser, and G. Birkl, “Reconfigurable site-selective manipulation of atomic quantum systems in two-dimensional arrays of dipole traps,” Physical Review A, vol. 81, no. 6, p. 060308, 2010.
  42. N. Y. Yao, L. Jiang, A. V. Gorshkov, P. C. Maurer, G. Giedke, J. I. Cirac, and M. D. Lukin, “Scalable architecture for a room temperature solid-state quantum information processor,” Nature communications, vol. 3, no. 1, p. 800, 2012.
  43. M. Kumph, M. Brownnutt, and R. Blatt, “2 dimensional arrays of rf ion traps with addressable interactions.”
  44. D. Crick, S. Donnellan, S. Ananthamurthy, R. Thompson, and D. Segal, “Fast shuttling of ions in a scalable penning trap array,” Review of scientific instruments, vol. 81, no. 1, 2010.
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