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Low-overhead quantum error correction codes with a cyclic topology
Published 6 Nov 2022 in quant-ph | (2211.03094v3)
Abstract: Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve performance with increasing the number of qubits involved. Here, we propose a resource-efficient scaling of a five-qubit perfect code with increasing-weight cyclic stabilizers for small distances on the ring architecture, which takes into account the topological features of the superconducting platform. We show an approach to construct the quantum circuit of a correction code with ancillas entangled with non-neighboring data qubits. Furthermore, we introduce a neural network-based decoding algorithm supported by an improved lookup table decoder and provide a numerical simulation of the proposed code, which demonstrates the exponential suppression of the logical error rate.
- A. Peres, Reversible logic and quantum computers, Phys. Rev. A 32, 3266 (1985).
- P. W. Shor, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52, R2493 (1995).
- A. R. Calderbank and P. W. Shor, Good quantum error-correcting codes exist, Physical Review A 54, 1098 (1996).
- E. Knill, R. Laflamme, and W. Zurek, Threshold accuracy for quantum computation (1996), arXiv:quant-ph/9610011 .
- A. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303, 2–30 (2003).
- B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys. 87, 307 (2015).
- D. P. DiVincenzo and P. W. Shor, Fault-tolerant error correction with efficient quantum codes, Phys. Rev. Lett. 77, 3260 (1996).
- A. M. Steane, Error correcting codes in quantum theory, Phys. Rev. Lett. 77, 793 (1996).
- D. Gottesman, Theory of fault-tolerant quantum computation, Phys. Rev. A 57, 127 (1998).
- Y. Tomita and K. M. Svore, Low-distance surface codes under realistic quantum noise, Phys. Rev. A 90, 062320 (2014).
- T. E. O’Brien, B. Tarasinski, and L. DiCarlo, Density-matrix simulation of small surface codes under current and projected experimental noise, npj Quantum Information 3, 39 (2017).
- R. Chao and B. W. Reichardt, Quantum error correction with only two extra qubits, Phys. Rev. Lett. 121, 050502 (2018).
- M. B. Hastings and J. Haah, Dynamically generated logical qubits, Quantum 5, 564 (2021).
- C. Gidney, M. Newman, and M. McEwen, Benchmarking the planar honeycomb code, Quantum 6, 813 (2022).
- Y. Takada and K. Fujii, Improving threshold for fault-tolerant color code quantum computing by flagged weight optimization (2024), arXiv:2402.13958 [quant-ph] .
- B. Domokos, Áron Márton, and J. K. Asbóth, Characterization of errors in a cnot between surface code patches (2024), arXiv:2405.05337 [quant-ph] .
- N. Schuch and J. Siewert, Natural two-qubit gate for quantum computation using the xy interaction, Physical Review A 67, 032301 (2003).
- I. A. Simakov, I. S. Besedin, and A. V. Ustinov, Simulation of the five-qubit quantum error correction code on superconducting qubits, Phys. Rev. A 105, 032409 (2022).
- A. V. Antipov, E. O. Kiktenko, and A. K. Fedorov, Realizing a class of stabilizer quantum error correction codes using a single ancilla and circular connectivity, Phys. Rev. A 107, 032403 (2023).
- A. A. Kovalev, I. Dumer, and L. P. Pryadko, Design of additive quantum codes via the code-word-stabilized framework, Phys. Rev. A 84, 062319 (2011).
- M. Grassl and T. Beth, Cyclic quantum error–correcting codes and quantum shift registers, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 456, 2689 (2000).
- H. Bombin and M. A. Martin-Delgado, Topological quantum distillation, Phys. Rev. Lett. 97, 180501 (2006).
- Y. Lin, S. Huang, and K. R. Brown, Single-shot error correction on toric codes with high-weight stabilizers, Phys. Rev. A 109, 052438 (2024).
- B. Srivastava, A. Frisk Kockum, and M. Granath, The XYZ2 hexagonal stabilizer code, Quantum 6, 698 (2022).
- S. Aaronson and D. Gottesman, Improved simulation of stabilizer circuits, Phys. Rev. A 70, 052328 (2004).
- C. Gidney, Stim: a fast stabilizer circuit simulator, Quantum 5, 497 (2021).
- D. Poulin and Y. Chung, On the iterative decoding of sparse quantum codes (2008), arXiv:0801.1241 [quant-ph] .
- S. Krastanov and L. Jiang, Deep neural network probabilistic decoder for stabilizer codes, Scientific reports 7, 11003 (2017).
- G. Torlai and R. G. Melko, Neural decoder for topological codes, Phys. Rev. Lett. 119, 030501 (2017).
- N. P. Breuckmann and X. Ni, Scalable Neural Network Decoders for Higher Dimensional Quantum Codes, Quantum 2, 68 (2018).
- C. Chamberland and P. Ronagh, Deep neural decoders for near term fault-tolerant experiments, Quantum Science and Technology 3, 044002 (2018).
- N. Maskara, A. Kubica, and T. Jochym-O’Connor, Advantages of versatile neural-network decoding for topological codes, Phys. Rev. A 99, 052351 (2019).
- R. W. J. Overwater, M. Babaie, and F. Sebastiano, Neural-network decoders for quantum error correction using surface codes: A space exploration of the hardware cost-performance tradeoffs, IEEE Transactions on Quantum Engineering 3, 1–19 (2022).
- Y.-H. Liu and D. Poulin, Neural belief-propagation decoders for quantum error-correcting codes, Phys. Rev. Lett. 122, 200501 (2019).
- S. Gicev, L. C. L. Hollenberg, and M. Usman, A scalable and fast artificial neural network syndrome decoder for surface codes, Quantum 7, 1058 (2023).
- S. Hochreiter and J. Schmidhuber, Long Short-Term Memory, Neural Computation 9, 1735 (1997).
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