Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and 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 144 tok/s
Gemini 2.5 Pro 50 tok/s Pro
GPT-5 Medium 24 tok/s Pro
GPT-5 High 28 tok/s Pro
GPT-4o 124 tok/s Pro
Kimi K2 210 tok/s Pro
GPT OSS 120B 433 tok/s Pro
Claude Sonnet 4.5 37 tok/s Pro
2000 character limit reached

Lift-Connected Surface Codes (2401.02911v2)

Published 5 Jan 2024 in quant-ph

Abstract: We use the recently introduced lifted product to construct a family of Quantum Low Density Parity Check Codes (QLDPC codes). The codes we obtain can be viewed as stacks of surface codes that are interconnected, leading to the name lift-connected surface (LCS) codes. LCS codes offer a wide range of parameters - a particularly striking feature is that they show interesting properties that are favorable compared to the standard surface code. For example, already at moderate numbers of physical qubits in the order of tens, LCS codes of equal size have lower logical error rate or similarly, require fewer qubits for a fixed target logical error rate. We present and analyze the construction and provide numerical simulation results for the logical error rate under code capacity and phenomenological noise. These results show that LCS codes attain thresholds that are comparable to corresponding (non-connected) copies of surface codes, while the logical error rate can be orders of magnitude lower, even for representatives with the same parameters. This provides a code family showing the potential of modern product constructions at already small qubit numbers. Their amenability to 3D-local connectivity renders them particularly relevant for near-term implementations.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (51)
  1. Google Quantum AI, Suppressing quantum errors by scaling a surface code logical qubit, Nature 614, 676 (2023).
  2. A. Y. Kitaev, Quantum computations: algorithms and error correction, Russian Mathematical Surveys 52, 1191 (1997).
  3. A. M. Stephens, Fault-tolerant thresholds for quantum error correction with the surface code, Phys. Rev. A 89, 022321 (2014).
  4. D. Gottesman, Fault-tolerant quantum computation with constant overhead, arXiv preprint arXiv:1310.2984 10.48550/arXiv.1310.2984 (2013).
  5. D. J. C. MacKay, G. Mitchison, and P. L. McFadden, Sparse-graph codes for quantum error correction, IEEE Trans. Inf. Theory 50, 2315 (2004).
  6. N. P. Breuckmann and J. N. Eberhardt, Quantum low-density parity-check codes, PRX Quantum 2, 040101 (2021a).
  7. J.-P. Tillich and G. Zémor, Quantum ldpc codes with positive rate and minimum distance proportional to the square root of the blocklength, IEEE Transactions on Information Theory 60, 1193 (2013).
  8. M. Sipser and D. A. Spielman, Expander codes, IEEE Trans. Inf. Theory 42, 1710 (1996).
  9. N. P. Breuckmann and J. N. Eberhardt, Balanced product quantum codes, IEEE Transactions on Information Theory 67, 6653 (2021b).
  10. P. Panteleev and G. Kalachev, Asymptotically good quantum and locally testable classical ldpc codes, in Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (2022) pp. 375–388.
  11. A. Leverrier and G. Zémor, Quantum tanner codes, arXiv preprint arXiv:2202.13641 10.48550/arXiv.2202.13641 (2022).
  12. S. Bravyi and B. Terhal, A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes, New Journal of Physics 11, 043029 (2009).
  13. S. Bravyi, D. Poulin, and B. Terhal, Tradeoffs for reliable quantum information storage in 2d systems, Phys. Rev. Lett. 104, 050503 (2010).
  14. N. Delfosse, M. E. Beverland, and M. A. Tremblay, Bounds on stabilizer measurement circuits and obstructions to local implementations of quantum ldpc codes, arXiv preprint arXiv:2109.14599  (2021).
  15. M. A. Tremblay, N. Delfosse, and M. E. Beverland, Constant-overhead quantum error correction with thin planar connectivity, Phys. Rev. Lett. 129, 050504 (2022).
  16. A. Strikis and L. Berent, Quantum low-density parity-check codes for modular architectures, PRX Quantum 4, 020321 (2023).
  17. M. Saffman, Quantum computing with atomic qubits and Rydberg interactions: progress and challenges, J. Phys. B: At. Mol. Opt. Phys. 49, 202001 (2016).
  18. S. A. Moses et al., A race track trapped-ion quantum processor, arXiv preprint arXiv:2305.03828  (2023), arXiv:2305.03828 [quant-ph] .
  19. P. Panteleev and G. Kalachev, Degenerate Quantum LDPC Codes With Good Finite Length Performance, Quantum 5, 585 (2021), 1904.02703v3 .
  20. N. Delfosse, V. Londe, and M. E. Beverland, Toward a Union-Find Decoder for Quantum LDPC Codes, IEEE Trans. Inf. Theory 68, 3187 (2022).
  21. A. Leverrier and G. Zémor, Efficient decoding up to a constant fraction of the code length for asymptotically good quantum codes, in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (Society for Industrial and Applied Mathematics, 2023) pp. 1216–1244.
  22. O. Higgott and N. P. Breuckmann, Improved Single-Shot Decoding of Higher-Dimensional Hypergraph-Product Codes, PRX Quantum 4, 020332 (2023).
  23. B. Eastin and E. Knill, Restrictions on transversal encoded quantum gate sets, Phys. Rev. Lett. 102, 110502 (2009).
  24. T. Jochym-O’Connor, A. Kubica, and T. J. Yoder, Disjointness of stabilizer codes and limitations on fault-tolerant logical gates, Physical Review X 8, 021047 (2018).
  25. N. P. Breuckmann and S. Burton, Fold-transversal clifford gates for quantum codes, arXiv preprint arXiv:2202.06647  (2022).
  26. T. Jochym-O’Connor, Fault-tolerant gates via homological product codes, Quantum 3, 120 (2019), 1807.09783v2 .
  27. A. Krishna and D. Poulin, Fault-tolerant gates on hypergraph product codes, Phys. Rev. X 11, 011023 (2021).
  28. A. O. Quintavalle, P. Webster, and M. Vasmer, Partitioning qubits in hypergraph product codes to implement logical gates, Quantum 7, 1153 (2023).
  29. P. Panteleev and G. Kalachev, Quantum ldpc codes with almost linear minimum distance, IEEE Transactions on Information Theory 68, 213 (2022b).
  30. R. Tanner, A recursive approach to low complexity codes, IEEE Transactions on Information Theory 27, 533 (1981).
  31. L. P. Pryadko, V. A. Shabashov, and V. K. Kozin, Qdistrnd: A gap package for computing the distance of quantum error-correcting codes, Journal of Open Source Software 7, 4120 (2022).
  32. A. G. Fowler, A. C. Whiteside, and L. C. L. Hollenberg, Towards Practical Classical Processing for the Surface Code, Phys. Rev. Lett. 108, 180501 (2012b).
  33. D. Poulin and Y. Chung, On the iterative decoding of sparse quantum codes, arXiv 10.48550/arXiv.0801.1241 (2008), 0801.1241 .
  34. A. J. Landahl, J. T. Anderson, and P. R. Rice, Fault-tolerant quantum computing with color codes, arXiv preprint arXiv:1108.5738  (2011).
  35. K. Jensen, J. G.r. Cardoso, and N. Sonnenschein, Optlang: An algebraic modeling language for mathematical optimization, Journal of Open Source Software 2, 139 (2017).
  36. A. Makhorin, Glpk (gnu linear programming kit) (2011).
  37. R. Gallager, Low-density parity-check codes, IRE Trans. Inf. Theory 8, 21 (1962).
  38. D. J. MacKay and R. M. Neal, Near shannon limit performance of low density parity check codes, Electronics letters 33, 457 (1997).
  39. J. Roffe, Quantum error correction: an introductory guide, Contemporary Physics 60, 226 (2019).
  40. J. Roffe, BP+OSD: A decoder for quantum LDPC codes (2022a).
  41. J. Roffe, LDPC: Python tools for low density parity check codes (2022b).
  42. J. Preskill, Fault-tolerant quantum computation, arXiv 10.48550/arXiv.quant-ph/9712048 (1997), quant-ph/9712048 .
  43. D. Aharonov and M. Ben-Or, Fault-tolerant quantum computation with constant error rate, SIAM Journal on Computing 38, 1207 (2008), https://doi.org/10.1137/S0097539799359385 .
  44. A. A. Kovalev and L. P. Pryadko, Fault tolerance of quantum low-density parity check codes with sublinear distance scaling, Phys. Rev. A 87, 020304 (2013).
  45. C. Wang, J. Harrington, and J. Preskill, Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory, Ann. Phys. 303, 31 (2003).
  46. T. Rakovszky and V. Khemani, The Physics of (good) LDPC Codes I. Gauging and dualities, arXiv 10.48550/arXiv.2310.16032 (2023), 2310.16032 .
  47. P. W. Shor, Fault-tolerant quantum computation, arXiv 10.48550/arXiv.quant-ph/9605011 (1996), quant-ph/9605011 .
  48. T. J. Yoder, R. Takagi, and I. L. Chuang, Universal fault-tolerant gates on concatenated stabilizer codes, Physical Review X 6, 031039 (2016).
  49. 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 2, 020341 (2021).
  50. A. G. Manes and J. Claes, Distance-preserving stabilizer measurements in hypergraph product codes, arXiv 10.48550/arXiv.2308.15520 (2023), 2308.15520 .
  51. C. Chamberland and M. E. Beverland, Flag fault-tolerant error correction with arbitrary distance codes, Quantum 2, 53 (2018).
Citations (4)
View on Semantic Scholar

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

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

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

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

Tweets

This paper has been mentioned in 2 tweets and received 11 likes.

Upgrade to Pro to view all of the tweets about this paper:

Start a free 7-day Pro trial