Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Facilitating Practical Fault-tolerant Quantum Computing Based on Color Codes (2309.05222v5)

Published 11 Sep 2023 in quant-ph

Abstract: Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical fault-tolerant quantum computing based on color codes. First, by introducing decoding graphs with error-rate-related weights, we obtained the threshold of $0.47\%$ of the 6,6,6 triangular color code under the standard circuit-level noise model, narrowing the gap to that of the surface code. Second, our work firstly investigates the circuit-level decoding of color code lattice surgery, and gives an efficient decoding algorithm, which is crucial for performing logical operations in a quantum computer with two-dimensional architectures. Lastly, a new state injection protocol of the triangular color code is proposed, reducing the output magic state error rate in one round of 15 to 1 distillation by two orders of magnitude compared to a previous rough protocol. We have also proven that our protocol offers the lowest logical error rates for state injection among all possible CSS codes.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (49)
  1. Peter W Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM review, 41(2):303–332, 1999.
  2. Richard P Feynman. Quantum mechanical computers. Optics news, 11(2):11–20, 1985.
  3. Simulation of topological field theories by quantum computers. Communications in Mathematical Physics, 227(3):587–603, 2002.
  4. John Preskill. Reliable quantum computers. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454(1969):385–410, 1998.
  5. Quantum computation and quantum information. Cambridge university press, 2010.
  6. Barbara M Terhal. Quantum error correction for quantum memories. Reviews of Modern Physics, 87(2):307, 2015.
  7. Daniel Gottesman. Stabilizer codes and quantum error correction. California Institute of Technology, 1997.
  8. Topological quantum memory. Journal of Mathematical Physics, 43(9):4452–4505, 2002.
  9. Jiannis K Pachos. Introduction to topological quantum computation. Cambridge University Press, 2012.
  10. Topological quantum distillation. Physical review letters, 97(18):180501, 2006.
  11. Aleksander Marek Kubica. The ABCs of the color code: A study of topological quantum codes as toy models for fault-tolerant quantum computation and quantum phases of matter. PhD thesis, California Institute of Technology, 2018.
  12. Surface codes: Towards practical large-scale quantum computation. Physical Review A, 86(3):032324, 2012.
  13. Quantum computing by color-code lattice surgery. arXiv preprint arXiv:1407.5103, 2014.
  14. Triangular color codes on trivalent graphs with flag qubits. New Journal of Physics, 22(2):023019, 2020.
  15. Towards practical classical processing for the surface code. Physical review letters, 108(18):180501, 2012.
  16. Ashley M Stephens. Fault-tolerant thresholds for quantum error correction with the surface code. Physical Review A, 89(2):022321, 2014.
  17. Surface code quantum computing by lattice surgery. New Journal of Physics, 14(12):123011, 2012.
  18. Low-overhead quantum computing with the color code. arXiv preprint arXiv:2201.07806, 2022.
  19. Daniel Litinski and Felix von Oppen. Lattice surgery with a twist: simplifying clifford gates of surface codes. Quantum, 2:62, 2018.
  20. Daniel Litinski. A game of surface codes: Large-scale quantum computing with lattice surgery. Quantum, 3:128, 2019.
  21. Low overhead quantum computation using lattice surgery. arXiv preprint arXiv:1808.06709, 2018.
  22. Circuit-level protocol and analysis for twist-based lattice surgery. Physical Review Research, 4(2):023090, 2022.
  23. Craig Gidney. Inplace access to the surface code y basis. arXiv preprint arXiv:2302.07395, 2023.
  24. Universal quantum computing with twist-free and temporally encoded lattice surgery. PRX Quantum, 3(1):010331, 2022.
  25. Universal quantum computation with ideal clifford gates and noisy ancillas. Physical Review A, 71(2):022316, 2005.
  26. Magic-state distillation with low overhead. Physical Review A, 86(5):052329, 2012.
  27. Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost. Physical Review A, 95(2):022316, 2017.
  28. Daniel Litinski. Magic state distillation: Not as costly as you think. Quantum, 3:205, 2019.
  29. Ying Li. A magic state’s fidelity can be superior to the operations that created it. New Journal of Physics, 17(2):023037, 2015.
  30. Magic state injection on the rotated surface code. In Proceedings of the 19th ACM International Conference on Computing Frontiers, pages 113–120, 2022.
  31. High-fidelity magic-state preparation with a biased-noise architecture. Physical Review A, 105(5):052410, 2022.
  32. Cost of universality: A comparative study of the overhead of state distillation and code switching with color codes. PRX Quantum, 2(2):020341, 2021.
  33. Nicolas Delfosse. Decoding color codes by projection onto surface codes. Physical Review A, 89(1):012317, 2014.
  34. Jack Edmonds. Paths, trees, and flowers. Canadian Journal of mathematics, 17:449–467, 1965.
  35. Oscar Higgott. Pymatching: A python package for decoding quantum codes with minimum-weight perfect matching. ACM Transactions on Quantum Computing, 3(3):1–16, 2022.
  36. Good quantum error-correcting codes exist. Physical Review A, 54(2):1098, 1996.
  37. Andrew Steane. Multiple-particle interference and quantum error correction. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 452(1954):2551–2577, 1996.
  38. Anyon condensation and the color code. arXiv preprint arXiv:2212.00042, 2022.
  39. Trading classical and quantum computational resources. Physical Review X, 6(2):021043, 2016.
  40. Austin G Fowler. Time-optimal quantum computation. arXiv preprint arXiv:1210.4626, 2012.
  41. Restrictions on transversal encoded quantum gate sets. Physical review letters, 102(11):110502, 2009.
  42. A fault-tolerant one-way quantum computer. Annals of physics, 321(9):2242–2270, 2006.
  43. Stacked codes: Universal fault-tolerant quantum computation in a two-dimensional layout. Physical Review A, 93(2):022323, 2016.
  44. Benjamin J Brown. A fault-tolerant non-clifford gate for the surface code in two dimensions. Science advances, 6(21):eaay4929, 2020.
  45. Fault-tolerant magic state preparation with flag qubits. Quantum, 3:143, 2019.
  46. Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits. npj Quantum Information, 6(1):91, 2020.
  47. The smallest code with transversal t. arXiv preprint arXiv:2210.14066, 2022.
  48. Surface code quantum computing with error rates over 1%. Physical Review A, 83(2):020302, 2011.
  49. Relaxing hardware requirements for surface code circuits using time-dynamics. arXiv preprint arXiv:2302.02192, 2023.
Citations (5)

Summary

We haven't generated a summary for this paper yet.

X Twitter Logo Streamline Icon: https://streamlinehq.com