- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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

Randomized Benchmarking with Non-Markovian Noise and Realistic Finite-Time Gates

Antoine Brillant1,*, Peter Groszkowski2, Alireza Seif3, Jens Koch4, and Aashish A. Clerk1,†

  • *Contact author: abrillant@uchicago.edu
  • †Contact author: aaclerk@uchicago.edu
PDF

Phys. Rev. Lett. 135, 070601 – Published 14 August, 2025

DOI: https://doi.org/10.1103/tmfd-qc5q

Abstract

We analyze the impact of non-Markovian classical noise on single-qubit randomized benchmarking experiments, in a manner that explicitly models the realization of each gate via realistic finite-duration pulses. Our new framework exploits the random nature of each gate sequence to derive expressions for the full survival probability decay curve which are nonperturbative in the noise strength. In the presence of non-Markovian noise, our approach shows that the decay curve can exhibit a strong dependence on the gate implementation method, with regimes of both exponential and power law decays. We discuss how these effects can complicate the interpretation of a randomized benchmarking experiment, but also how to leverage them to probe non-Markovianity.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (35)

  1. E. Knill, D. Leibfried, R. Reichle, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, Phys. Rev. A 77, 012307 (2008).
  2. E. Magesan, J. M. Gambetta, and J. Emerson, Phys. Rev. Lett. 106, 180504 (2011).
  3. E. Magesan, J. M. Gambetta, and J. Emerson, Phys. Rev. A 85, 042311 (2012).
  4. J. Helsen, I. Roth, E. Onorati, A. H. Werner, and J. Eisert, PRX Quantum 3, 020357 (2022).
  5. A. Hashim, L. B. Nguyen, N. Goss, B. Marinelli, R. K. Naik, T. Chistolini, J. Hines, J. P. Marceaux, Y. Kim, P. Gokhale, T. Tomesh, S. Chen, L. Jiang, S. Ferracin, K. Rudinger, T. Proctor, K. C. Young, R. Blume-Kohout, and I. Siddiqi, arXiv:2408.12064.
  6. Y. Kim, L. C. G. Govia, A. Dane, E. van den Berg, D. M. Zajac, B. Mitchell, Y. Liu, K. Balakrishnan, G. Keefe, A. Stabile, E. Pritchett, J. Stehlik, and A. Kandala, arXiv:2407.02467.
  7. K. X. Wei, E. Pritchett, D. M. Zajac, D. C. McKay, and S. Merkel, Phys. Rev. Appl. 21, 024018 (2024).
  8. E. Paladino, Y. M. Galperin, G. Falci, and B. L. Altshuler, Rev. Mod. Phys. 86, 361 (2014).
  9. M. Veldhorst, J. C. C. Hwang, C. H. Yang, A. W. Leenstra, B. de Ronde, J. P. Dehollain, J. T. Muhonen, F. E. Hudson, K. M. Itoh, A. Morello, and A. S. Dzurak, Nat. Nanotechnol. 9, 981 (2014).
  10. C. A. Ryan, M. Laforest, and R. Laflamme, New J. Phys. 11, 013034 (2009).
  11. P. Figueroa-Romero, K. Modi, and M.-H. Hsieh, Quantum 6, 868 (2022).
  12. B. H. Fong and S. T. Merkel, arXiv:1703.09747.
  13. P. Figueroa-Romero, K. Modi, R. J. Harris, T. M. Stace, and M.-H. Hsieh, PRX Quantum 2, 040351 (2021).
  14. M. A. Fogarty, M. Veldhorst, R. Harper, C. H. Yang, S. D. Bartlett, S. T. Flammia, and A. S. Dzurak, Phys. Rev. A 92, 022326 (2015).
  15. H. Ball, T. M. Stace, S. T. Flammia, and M. J. Biercuk, Phys. Rev. A 93, 022303 (2016).
  16. C. L. Edmunds, C. Hempel, R. J. Harris, V. Frey, T. M. Stace, and M. J. Biercuk, Phys. Rev. Res. 2, 013156 (2020).
  17. X. Zhang, Z. Wu, G. A. L. White, Z. Xiang, S. Hu, Z. Peng, Y. Liu, D. Zheng, X. Fu, A. Huang, D. Poletti, K. Modi, J. Wu, M. Deng, and C. Guo, Randomised benchmarking for characterizing and forecasting correlated processes (2023) [arXiv:2312.06062].
  18. P. Groszkowski, A. Seif, J. Koch, and A. A. Clerk, Quantum 7, 972 (2023).
  19. N. G. Van Kampen, Physica (Amsterdam) 74, 215 (1974).
  20. N. G. Van Kampen, Physica (Amsterdam) 74, 239 (1974).
  21. T. Proctor, K. Rudinger, K. Young, M. Sarovar, and R. Blume-Kohout, Phys. Rev. Lett. 119, 130502 (2017).
  22. J. J. Wallman and J. Emerson, Phys. Rev. A 94, 052325 (2016).
  23. See Supplemental Material at http://link.aps.org/supplemental/10.1103/tmfd-qc5q [5,18–20,22,24–27] graining approximation and extension to other systems involving random gate sequences.
  24. R. F. Fox, J. Math. Phys. (N.Y.) 17, 1148 (1976).
  25. R. Kubo, J. Phys. Soc. Jpn. 17, 1100 (1962).
  26. A. Winick, J. J. Wallman, D. Dahlen, I. Hincks, E. Ospadov, and J. Emerson, arXiv:2212.07500.
  27. A. A. Mele, Quantum 8, 1340 (2024).
  28. K. Serniak, M. Hays, G. de Lange, S. Diamond, S. Shankar, L. D. Burkhart, L. Frunzio, M. Houzet, and M. H. Devoret, Phys. Rev. Lett. 121, 157701 (2018).
  29. L. Viola and E. Knill, Phys. Rev. Lett. 94, 060502 (2005).

  30. This is a consequence of our assumption that the initial state of the qubit is uncorrelated with the noise.

  31. Y. Zhang and M. I. Dykman, Phys. Rev. B 92, 165419 (2015).
  32. J. M. Epstein, A. W. Cross, E. Magesan, and J. M. Gambetta, Phys. Rev. A 89, 062321 (2014).

  33. This crossover between two kinds of decay is reminiscent of (but distinct from) the findings in Ref. [14], where RB decay was described by a sum of two exponential terms.

  34. A. Erhard, J. J. Wallman, L. Postler, M. Meth, R. Stricker, E. A. Martinez, P. Schindler, T. Monz, J. Emerson, and R. Blatt, Nat. Commun. 10, 5347 (2019).
  35. https://www.energy.gov/doe-public-access-plan

Outline

Information

Phys. Rev. Lett. 135, 070601– Published 14 August, 2025
  • Received 20 January 2025
  • Revised 20 May 2025
  • Accepted 27 June 2025
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