Papers
Topics
Authors
Recent
Detailed Answer
Quick Answer
Concise responses based on abstracts only
Detailed Answer
Well-researched responses based on abstracts and relevant paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses
Gemini 2.5 Flash
Gemini 2.5 Flash 63 tok/s
Gemini 2.5 Pro 49 tok/s Pro
GPT-5 Medium 14 tok/s Pro
GPT-5 High 19 tok/s Pro
GPT-4o 100 tok/s Pro
Kimi K2 174 tok/s Pro
GPT OSS 120B 472 tok/s Pro
Claude Sonnet 4 37 tok/s Pro
2000 character limit reached

Concatenated Steane code with single-flag syndrome checks (2403.09978v3)

Published 15 Mar 2024 in quant-ph

Abstract: A fault-tolerant error correction (FTEC) protocol with a high error suppression rate and low overhead is very desirable for the near-term implementation of quantum computers. In this work, we develop a distance-preserving flag FTEC protocol for the [[49,1,9]] concatenated Steane code, which requires only two ancilla qubits per generator and can be implemented on a planar layout. We generalize the weight-parity error correction (WPEC) technique from [Phys. Rev. A 104, 042410 (2021)] and find a gate ordering of flag circuits for the concatenated Steane code which makes syndrome extraction with two ancilla qubits per generator possible. The FTEC protocol is constructed using the optimization tools for flag FTEC developed in [PRX Quantum 5, 020336 (2024)] and is simulated under the circuit-level noise model without idling noise. Our simulations give a pseudothreshold of $1.64 \times 10{-3}$ for the [[49,1,9]] concatenated Steane code, which is better than a pseudothreshold of $1.43 \times 10{-3}$ for the [[61,1,9]] 6.6.6 color code simulated under the same settings. This is in contrast to the code capacity model where the [[61,1,9]] code performs better.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (42)
  1. T. Tansuwannont and D. Leung, “Fault-tolerant quantum error correction using error weight parities,” Physical Review A, vol. 104, no. 4, p. 042410, 2021.
  2. B. Pato, T. Tansuwannont, S. Huang, and K. R. Brown, “Distance-preserving flag fault-tolerant protocols for planar color codes of distance 9,” preprint arXiv:2306.12862, 2023.
  3. P. W. Shor, “Fault-tolerant quantum computation,” Proceedings., 37th Annual Symposium on Foundations of Computer Science, pp. 56–65, 1996.
  4. D. Gottesman, Stabilizer Codes and Quantum Error Correction. PhD thesis, California Institute of Technology, 1997.
  5. A. M. Steane, “Active stabilization, quantum computation, and quantum state synthesis,” Physical Review Letters, vol. 78, no. 11, p. 2252, 1997.
  6. E. Knill and R. Laflamme, “Theory of quantum error-correcting codes,” Physical Review A, vol. 55, no. 2, p. 900, 1997.
  7. R. Chao and B. W. Reichardt, “Quantum error correction with only two extra qubits,” Physical Review Letters, vol. 121, no. 5, p. 050502, 2018.
  8. R. Chao and B. W. Reichardt, “Flag fault-tolerant error correction for any stabilizer code,” PRX Quantum, vol. 1, no. 1, p. 010302, 2020.
  9. C. Chamberland, A. Kubica, T. J. Yoder, and G. Zhu, “Triangular color codes on trivalent graphs with flag qubits,” New Journal of Physics, vol. 22, no. 2, p. 023019, 2020.
  10. M. E. Beverland, A. Kubica, and K. M. Svore, “Cost of universality: A comparative study of the overhead of state distillation and code switching with color codes,” PRX Quantum, vol. 2, no. 2, p. 020341, 2021.
  11. A. J. Landahl, J. T. Anderson, and P. R. Rice, “Fault-tolerant quantum computing with color codes,” preprint arXiv:1108.5738, 2011.
  12. N. Delfosse, “Decoding color codes by projection onto surface codes,” Physical Review A, vol. 89, p. 012317, Jan 2014.
  13. C. Gidney and C. Jones, “New circuits and an open source decoder for the color code,” preprint arXiv:2312.08813, 2023.
  14. A. Morvan et al., “Phase transition in random circuit sampling,” Dec. 2023. arXiv:2304.11119 [quant-ph].
  15. Y. Kim, A. Eddins, S. Anand, K. X. Wei, E. van den Berg, S. Rosenblatt, H. Nayfeh, Y. Wu, M. Zaletel, K. Temme, and A. Kandala, “Evidence for the utility of quantum computing before fault tolerance,” Nature, vol. 618, p. 500–505, June 2023.
  16. Y. Wang, S. Simsek, T. M. Gatterman, J. A. Gerber, K. Gilmore, D. Gresh, N. Hewitt, C. V. Horst, M. Matheny, T. Mengle, B. Neyenhuis, and B. Criger, “Fault-tolerant one-bit addition with the smallest interesting colour code,” Sept. 2023. arXiv:2309.09893 [quant-ph].
  17. D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter, J. P. B. Ataides, N. Maskara, I. Cong, X. Gao, P. S. Rodriguez, T. Karolyshyn, G. Semeghini, M. J. Gullans, M. Greiner, V. Vuletic, and M. D. Lukin, “Logical quantum processor based on reconfigurable atom arrays,” Nature, vol. 626, p. 58–65, Feb. 2024.
  18. D. Aharonov and M. Ben-Or, “Fault-tolerant quantum computation with constant error rate,” SIAM Journal on Computing, 2008.
  19. J. Preskill, “Reliable quantum computers,” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 454, no. 1969, pp. 385–410, 1998.
  20. E. Knill, R. Laflamme, and W. H. Zurek, “Threshold accuracy for quantum computation,” arXiv: quant-ph/9610011, 1996.
  21. P. Aliferis, D. Gottesman, and J. Preskill, “Quantum accuracy threshold for concatenated distance-3 codes,” Quantum Information and Computation, vol. 6, no. 2, pp. 97–165, 2006.
  22. D. Poulin, “Optimal and efficient decoding of concatenated quantum block codes,” Physical Review A, vol. 74, p. 052333, Nov 2006.
  23. C. Chamberland and M. E. Beverland, “Flag fault-tolerant error correction with arbitrary distance codes,” Quantum, vol. 2, p. 53, Feb. 2018.
  24. T. Tansuwannont, C. Chamberland, and D. Leung, “Flag fault-tolerant error correction, measurement, and quantum computation for cyclic Calderbank-Shor-Steane codes,” Physical Review A, vol. 101, no. 1, p. 012342, 2020.
  25. R. Chao and B. W. Reichardt, “Fault-tolerant quantum computation with few qubits,” npj Quantum Information, vol. 4, no. 1, p. 42, 2018.
  26. C. Chamberland and A. W. Cross, “Fault-tolerant magic state preparation with flag qubits,” Quantum, vol. 3, p. 143, 2019.
  27. H. Bombin and M. A. Martin-Delgado, “Topological quantum distillation,” Physical Review Letters, vol. 97, no. 18, p. 180501, 2006.
  28. E. Sabo, A. B. Aloshious, and K. R. Brown, “Trellis decoding for qudit stabilizer codes and its application to qubit topological codes,” preprint arXiv:2106.08251, 2022.
  29. A. Steane, “Multiple-particle interference and quantum error correction,” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 452, no. 1954, pp. 2551–2577, 1996.
  30. A. R. Calderbank and P. W. Shor, “Good quantum error-correcting codes exist,” Physical Review A, vol. 54, no. 2, p. 1098, 1996.
  31. For the formal definition of FTEC, refer to the revised definition of FTEC in [32] which is extended from the definition in [21]; see also [2] for definition comparison.
  32. T. Tansuwannont and D. Leung, “Achieving fault tolerance on capped color codes with few ancillas,” PRX Quantum, vol. 3, no. 3, p. 030322, 2022.
  33. T. Tansuwannont, B. Pato, and K. R. Brown, “Adaptive syndrome measurements for Shor-style error correction,” Quantum, vol. 7, p. 1075, Aug. 2023.
  34. Cirq Developers, “Cirq v1.1.0,” 2022. Full list of authors: https://github.com/quantumlib/Cirq, Zenodo, doi:10.5281/zenodo.7465577.
  35. C. Gidney, “Stim: a fast stabilizer circuit simulator,” Quantum, vol. 5, p. 497, July 2021.
  36. S. Huang, K. R. Brown, and M. Cetina, “Comparing shor and steane error correction using the bacon-shor code,” Dec. 2023. arXiv:2312.10851 [quant-ph].
  37. L. Egan, D. M. Debroy, C. Noel, et al., “Fault-tolerant control of an error-corrected qubit,” Nature, vol. 598, pp. 281–286, Oct. 2021.
  38. L. Postler, F. Butt, I. Pogorelov, C. D. Marciniak, S. Heußen, R. Blatt, P. Schindler, M. Rispler, M. Müller, and T. Monz, “Demonstration of fault-tolerant steane quantum error correction,” Dec. 2023. arXiv:2312.09745 [quant-ph].
  39. C. Ryan-Anderson, N. C. Brown, M. S. Allman, B. Arkin, G. Asa-Attuah, C. Baldwin, J. Berg, J. G. Bohnet, S. Braxton, N. Burdick, J. P. Campora, A. Chernoguzov, J. Esposito, B. Evans, D. Francois, J. P. Gaebler, T. M. Gatterman, J. Gerber, K. Gilmore, D. Gresh, A. Hall, A. Hankin, J. Hostetter, D. Lucchetti, K. Mayer, J. Myers, B. Neyenhuis, J. Santiago, J. Sedlacek, T. Skripka, A. Slattery, R. P. Stutz, J. Tait, R. Tobey, G. Vittorini, J. Walker, and D. Hayes, “Implementing fault-tolerant entangling gates on the five-qubit code and the color code,” Aug. 2022. arXiv:2208.01863 [quant-ph].
  40. H. Yamasaki and M. Koashi, “Time-efficient constant-space-overhead fault-tolerant quantum computation,” Nature Physics, vol. 20, p. 247–253, Feb. 2024.
  41. S. Yoshida, S. Tamiya, and H. Yamasaki, “Concatenate codes, save qubits,” Feb. 2024. arXiv:2402.09606 [quant-ph].
  42. A code for our proof is published in a Colab python notebook: https://colab.research.google.com/drive/ 115qVvd8zvEF8JikAHIKLtnGuTrjsMUZR.
Citations (2)
View on Semantic Scholar
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Summary

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

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Dice Question Streamline Icon: https://streamlinehq.com

Follow-Up Questions

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets