- Physical Review Journals
All JournalsPhysics Magazine

Physical Review A

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Resilience of the surface code to error bursts

Shi Jie Samuel Tan1,2, Christopher A. Pattison3, Matt McEwen4, and John Preskill3,5

PDF

Phys. Rev. A 113, 022450 – Published 26 February, 2026

DOI: https://doi.org/10.1103/vwtl-hwfx

Abstract

Quantum error correction works effectively only if the error rate of gate operations is sufficiently low. However, some rare physical mechanisms can cause a temporary increase in the error rate that affects many qubits; examples include ionizing radiation in superconducting hardware and large deviations in the global control of atomic systems. We refer to such rare transient spikes in the gate error rate as error bursts. In this work, we investigate the resilience of the rotated surface code to generic error bursts. We assume that, after appropriate mitigation strategies, the spike in the error rate lasts for only a single syndrome-extraction cycle; we also assume that the enhanced error rate is uniform across the code block. Under these assumptions, and for a circuit-level depolarizing noise model, we perform Monte Carlo simulations to determine the regime in burst error rate and background error rate for which the memory time becomes arbitrarily long as the code block size grows. Our results indicate that suitable hardware mitigation methods combined with standard decoding methods may suffice to protect against transient error bursts in the rotated surface code.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (42)

  1. S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary, arXiv:quant-ph/9811052.
  2. E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topological quantum memory, J. Math. Phys. 43, 4452 (2002).
  3. J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A 76, 042319 (2007).
  4. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  5. Google Quantum AI, Suppressing quantum errors by scaling a surface code logical qubit, Nature (London) 614, 676 (2023).
  6. L. Cardani, I. Colantoni, A. Cruciani, F. De Dominicis, G. D'Imperio, M. Laubenstein, A. Mariani, L. Pagnanini, S. Pirro, C. Tomei, et al., Disentangling the sources of ionizing radiation in superconducting qubits, Eur. Phys. J. C 83, 94 (2023).
  7. M. McEwen, L. Faoro, K. Arya, A. Dunsworth, T. Huang, S. Kim, B. Burkett, A. Fowler, F. Arute, J. C. Bardin, et al., Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits, Nat. Phys. 18, 107 (2022).
  8. Q. Xu, A. Seif, H. Yan, N. Mannucci, B. O. Sane, R. Van Meter, A. N. Cleland, and L. Jiang, Distributed quantum error correction for chip-level catastrophic errors, Phys. Rev. Lett. 129, 240502 (2022).
  9. C. A. Pattison, A. Krishna, and J. Preskill, Hierarchical memories: Simulating quantum LDPC codes with local gates, Quantum 9, 1728 (2025).
  10. J. M. Martinis, Saving superconducting quantum processors from decay and correlated errors generated by gamma and cosmic rays, npj Quantum Inf. 7, 90 (2021).
  11. D. Gottesman, Stabilizer codes and quantum error correction, arXiv:quant-ph/9705052.
  12. C. D. Wilen, S. Abdullah, N. A. Kurinsky, C. Stanford, L. Cardani, G. D'Imperio, C. Tomei, L. Faoro, L. B. Ioffe, C. H. Liu, A. Opremcak, B. G. Christensen, J. L. DuBois, and R. McDermott, Correlated charge noise and relaxation errors in superconducting qubits, Nature (London) 594, 369 (2021).
  13. M. McEwen, K. C. Miao, J. Atalaya, A. Bilmes, A. Crook, J. Bovaird, J. M. Kreikebaum, N. Zobrist, E. Jeffrey, B. Ying, A. Bengtsson, H.-S. Chang, A. Dunsworth, J. Kelly, Y. Zhang, E. Forati, R. Acharya, J. Iveland, W. Liu, S. Kim, et al., Resisting high-energy impact events through gap engineering in superconducting qubit arrays, Phys. Rev. Lett. 133, 240601 (2024).
  14. P. M. Harrington, M. Li, M. Hays, W. V. D. Pontseele, D. Mayer, H. D. Pinckney, F. Contipelli, M. Gingras, B. M. Niedzielski, H. Stickler, J. L. Yoder, M. E. Schwartz, J. A. Grover, K. Serniak, W. D. Oliver, and J. A. Formaggio, Synchronous detection of cosmic rays and correlated errors in superconducting qubit arrays, Nat. Commun. 16, 6428 (2025).
  15. V. Iaia, J. Ku, A. Ballard, C. Larson, E. Yelton, C. Liu, S. Patel, R. McDermott, and B. Plourde, Phonon downconversion to suppress correlated errors in superconducting qubits, Nat. Commun. 13, 6425 (2022).
  16. V. D. Kurilovich, G. Roberts, L. S. Martin, M. McEwen, A. Eickbusch, L. Faoro, L. B. Ioffe, J. Atalaya, A. Bilmes, J. M. Kreikebaum, A. Bengtsson, P. Klimov, M. Neeley, W. Mruczkiewicz, K. Miao, I. L. Aleiner, J. Kelly, Y. Chen, K. Satzinger, and A. Opremcak, Correlated error bursts in a gap-engineered superconducting qubit array, arXiv:2506.18228.
  17. J. D. Chadwick, C. Kang, J. Viszlai, S. F. Lin, and F. T. Chong, Averting multi-qubit burst errors in surface code magic state factories, in IEEE International Conference on Quantum Computing and Engineering (QCE), Montreal, QC, Canada (IEEE, Piscataway, NJ, 2024), pp. 1089–1101.
  18. A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012).
  19. C. Gidney, Stim: a fast stabilizer circuit simulator, Quantum 5, 497 (2021).
  20. N. Delfosse and N. H. Nickerson, Almost-linear time decoding algorithm for topological codes, Quantum 5, 595 (2021).
  21. O. Higgott and C. Gidney, Sparse blossom: Correcting a million errors per core second with minimum-weight matching, Quantum 9, 1600 (2025).
  22. O. Higgott and C. Gidney, Pymatching v2, https://github.com/oscarhiggott/PyMatching.
  23. D. Horsman, A. G. Fowler, S. Devitt, and R. Van Meter, Surface code quantum computing by lattice surgery, New J. Phys. 14, 123011 (2012).
  24. C. T. Chubb and S. T. Flammia, Statistical mechanical models for quantum codes with correlated noise, Ann. Inst. Henri Poincare D 8, 269 (2021).
  25. J. Ramette, J. Sinclair, N. P. Breuckmann, and V. Vuletić, Fault-tolerant connection of error-corrected qubits with noisy links, npj Quantum Inf. 10, 58 (2024).
  26. A. G. Fowler, D. S. Wang, C. D. Hill, T. D. Ladd, R. Van Meter, and L. C. L. Hollenberg, Surface code quantum communication, Phys. Rev. Lett. 104, 180503 (2010).
  27. C. Gidney, M. Newman, A. Fowler, and M. Broughton, A fault-tolerant honeycomb memory, Quantum 5, 605 (2021).
  28. Google Quantum AI, Exponential suppression of bit or phase errors with cyclic error correction, Nature (London) 595, 383 (2021).
  29. C. A. Pattison, M. E. Beverland, M. P. da Silva, and N. Delfosse, Improved quantum error correction using soft information, arXiv:2107.13589.
  30.  A rotated surface code only requires 2d2−1, however, a regular tiling of surface codes will require an extra qubit.
  31. M. Lenander, H. Wang, R. C. Bialczak, E. Lucero, M. Mariantoni, M. Neeley, A. O'Connell, D. Sank, M. Weides, J. Wenner, et al., Measurement of energy decay in superconducting qubits from nonequilibrium quasiparticles, Phys. Rev. B 84, 024501 (2011).
  32. T. Thorbeck, A. Eddins, I. Lauer, D. T. McClure, and M. Carroll, Two-level-system dynamics in a superconducting qubit due to background ionizing radiation, PRX Quantum 4, 020356 (2023).
  33. An extremely large global coherent error deviates from our definition of an error burst as elevated independent noise, but moderately large coherent errors are approximately captured by our definition.
  34. S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. Manovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara, et al., High-fidelity parallel entangling gates on a neutral-atom quantum computer, Nature (London) 622, 268 (2023).
  35. P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp, M. Steiner, V. Jacques, G. Balasubramanian, M. Markham, D. Twitchen, et al., Quantum register based on coupled electron spins in a room-temperature solid, Nat. Phys. 6, 249 (2010).
  36. C. E. Bradley, J. Randall, M. H. Abobeih, R. C. Berrevoets, M. J. Degen, M. A. Bakker, M. Markham, D. J. Twitchen, and T. H. Taminiau, A ten-qubit solid-state spin register with quantum memory up to one minute, Phys. Rev. X 9, 031045 (2019).
  37. M. H. Abobeih, Y. Wang, J. Randall, S. Loenen, C. E. Bradley, M. Markham, D. J. Twitchen, B. M. Terhal, and T. H. Taminiau, Fault-tolerant operation of a logical qubit in a diamond quantum processor, Nature (London) 606, 884 (2022).
  38. F. A. Zwanenburg, A. S. Dzurak, A. Morello, M. Y. Simmons, L. C. L. Hollenberg, G. Klimeck, S. Rogge, S. N. Coppersmith, and M. A. Eriksson, Silicon quantum electronics, Rev. Mod. Phys. 85, 961 (2013).
  39. C. D. Hill, E. Peretz, S. J. Hile, M. G. House, M. Fuechsle, S. Rogge, M. Y. Simmons, and L. C. Hollenberg, A surface code quantum computer in silicon, Sci. Adv. 1, e1500707 (2015).
  40. M. Veldhorst, H. Eenink, C.-H. Yang, and A. S. Dzurak, Silicon CMOS architecture for a spin-based quantum computer, Nat. Commun. 8, 1766 (2017).
  41. M. Halldórsson and J. Radhakrishnan, Greed is good: Approximating independent sets in sparse and bounded-degree graphs, in Proceedings of the Twenty-Sixth Annual ACM Symposium on Theory of Computing (Association for Computing Machinery, New York, 1994), pp. 439–448.
  42. 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).

Outline

Information

Phys. Rev. A 113, 022450– Published 26 February, 2026
  • Received 16 October 2025
  • Accepted 5 January 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation