Papers
Topics
Authors
Recent
Search
2000 character limit reached

Partial Syndrome Measurement for Hypergraph Product Codes

Published 29 Jun 2023 in quant-ph | (2306.17122v3)

Abstract: Hypergraph product codes are a promising avenue to achieving fault-tolerant quantum computation with constant overhead. When embedding these and other constant-rate qLDPC codes into 2D, a significant number of nonlocal connections are required, posing difficulties for some quantum computing architectures. In this work, we introduce a fault-tolerance scheme that aims to alleviate the effects of implementing this nonlocality by measuring generators acting on spatially distant qubits less frequently than those which do not. We investigate the performance of a simplified version of this scheme, where the measured generators are randomly selected. When applied to hypergraph product codes and a modified small-set-flip decoding algorithm, we prove that for a sufficiently high percentage of generators being measured, a threshold still exists. We also find numerical evidence that the logical error rate is exponentially suppressed even when a large constant fraction of generators are not measured.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (34)
  1. D. Aharonov and M. Ben-Or, Fault-Tolerant Quantum Computation With Constant Error Rate, arXiv:quant-ph/9906129 (1999) arXiv:quant-ph/9906129 type: article.
  2. A. Y. Kitaev, Quantum computations: algorithms and error correction, Russian Mathematical Surveys 52, 1191 (1997).
  3. D. Gottesman, Fault-tolerant quantum computation with constant overhead, Quantum Info. Comput. 14, 1338–1372 (2014).
  4. N. P. Breuckmann and J. N. Eberhardt, Balanced product quantum codes, IEEE Transactions on Information Theory 67, 6653 (2021).
  5. P. Panteleev and G. Kalachev, Asymptotically good quantum and locally testable classical ldpc codes 10.48550/arXiv.2111.03654 (2022), arXiv:2111.03654 [quant-ph].
  6. A. Leverrier and G. Zémor, Quantum tanner codes 10.48550/arXiv.2202.13641 (2022), arXiv:2202.13641 [quant-ph].
  7. T.-C. Lin and M.-H. Hsieh, Good quantum ldpc codes with linear time decoder from lossless expanders 10.48550/arXiv.2203.03581 (2022), arXiv:2203.03581 [quant-ph].
  8. S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary (1998), arXiv:quant-ph/9811052 [quant-ph] .
  9. A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303, 2–30 (2003), arXiv:quant-ph/9707021.
  10. 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 (2014).
  11. 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), arXiv:0810.1983 [cond-mat, physics:quant-ph].
  12. S. Bravyi, D. Poulin, and B. Terhal, Tradeoffs for reliable quantum information storage in 2d systems, Physical Review Letters 104, 050503 (2010), arXiv:0909.5200 [quant-ph].
  13. N. Baspin and A. Krishna, Quantifying nonlocality: How outperforming local quantum codes is expensive, Physical Review Letters 129, 10.1103/physrevlett.129.050505 (2022a).
  14. N. Baspin and A. Krishna, Connectivity constrains quantum codes, Quantum 6, 711 (2022b).
  15. N. Delfosse, M. E. Beverland, and M. A. Tremblay, Bounds on stabilizer measurement circuits and obstructions to local implementations of quantum ldpc codes,   (2021), arXiv:2109.14599 [quant-ph].
  16. N. Baspin, O. Fawzi, and A. Shayeghi, A lower bound on the overhead of quantum error correction in low dimensions (2023), arXiv:2302.04317 [quant-ph] .
  17. D. Gottesman, Stabilizer codes and quantum error correction, arXiv:quant-ph/9705052  (1997), arXiv: quant-ph/9705052.
  18. A. R. Calderbank and P. W. Shor, Good quantum error-correcting codes exist, Physical Review A 54, 1098–1105 (1996), arXiv: quant-ph/9512032.
  19. M. Sipser and D. Spielman, Expander codes, IEEE Transactions on Information Theory 42, 1710–1722 (1996).
  20. A. Leverrier, J.-P. Tillich, and G. Zemor, Quantum expander codes, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science , 810–824 (2015), arXiv: 1504.00822.
  21. O. Fawzi, A. Grospellier, and A. Leverrier, Efficient decoding of random errors for quantum expander codes, in Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing (ACM, 2018).
  22. D. Gottesman, Opportunities and challenges in fault-tolerant quantum computation, arXiv:quant-ph/2210.15844  (2022), arXiv:quant-ph/2210.15844.
  23. O. Fawzi, A. Grospellier, and A. Leverrier, Constant overhead quantum fault-tolerance with quantum expander codes, in 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS) (IEEE, 2018).
  24. A. Grospellier, Constant time decoding of quantum expander codes and application to fault-tolerant quantum computation, Theses, Sorbonne Université (2019).
  25. A. Grospellier and A. Krishna, Numerical study of hypergraph product codes, arXiv:1810.03681 [quant-ph]  (2019), arXiv: 1810.03681.
  26. Z. Chen et al., Exponential suppression of bit or phase errors with cyclic error correction, Nature 595, 383–387 (2021).
  27. N. P. Breuckmann and B. M. Terhal, Constructions and noise threshold of hyperbolic surface codes, IEEE Transactions on Information Theory 62, 3731 (2016).
  28. O. Higgott and C. Gidney, Sparse blossom: correcting a million errors per core second with minimum-weight matching (2023), arXiv:2303.15933 [quant-ph] .
  29. H. Bombín, Single-shot fault-tolerant quantum error correction, Physical Review X 5, 031043 (2015).
  30. E. T. Campbell, A theory of single-shot error correction for adversarial noise, Quantum Science and Technology 4, 025006 (2019), arXiv:1805.09271 [quant-ph].
  31. L. Guth and A. Lubotzky, Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds, Journal of Mathematical Physics 55, 10.1063/1.4891487 (2014), 082202, https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/1.4891487/15617383/082202_1_online.pdf .
  32. M. B. Hastings, Decoding in hyperbolic spaces: Ldpc codes with linear rate and efficient error correction (2013), arXiv:1312.2546 [quant-ph] .
  33. N. P. Breuckmann and V. Londe, Single-shot decoding of linear rate LDPC quantum codes with high performance, IEEE Trans. Inf. Theory 68, 272 (2022).
  34. P. Panteleev and G. Kalachev, Degenerate quantum LDPC codes with good finite length performance, Quantum 5, 585 (2021).
Citations (9)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

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

Generate Now

Continue Learning

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

Generate Now

Collections

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

Sign Up

Tweets

Sign up for free to view the 1 tweet with 0 likes about this paper.

Sign Up for Free