- Physical Review Journals
All JournalsPhysics Magazine

PRX Quantum

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

Logical Accreditation: A Framework for Efficient Certification of Fault-Tolerant Computations

James Mills1,*, Adithya Sireesh1, Dominik Leichtle1, Joschka Roffe1, and Elham Kashefi1,2

  • *Contact author: J.Mills-7@sms.ed.ac.uk
PDF

PRX Quantum 7, 033053 – Published 11 September, 2026

DOI: https://doi.org/10.1103/7pj4-gcbq

Abstract

As fault-tolerant quantum computers scale, certifying the accuracy of computations performed with encoded logical qubits will soon become classically intractable. This creates a critical need for scalable, device-independent certification methods. In this work, we introduce logical accreditation, a framework for efficiently certifying the correctness of quantum computations performed on logical qubits. Our protocol is robust against general noise models, far beyond those typically considered in performance analyses of quantum error-correcting codes. Through numerical simulations, we demonstrate that logical accreditation can scalably certify quantum advantage experiments and indicate the crossover point where encoded computations begin to outperform physical computations. The framework also enables evaluation of whether logical error rates are sufficiently low that error mitigation can be efficiently performed, extends entropy benchmarking to the regime of fault-tolerant computation, and upper bounds the infidelity of the logical output state of a computation. Underlying the framework is a novel randomized compilation scheme that converts arbitrary logical circuit noise into stochastic Pauli noise. This scheme includes a method for twirling non-transversal logical gates beyond the standard T gate, resolving an open problem posed by [Piveteau et al. PRL 127, 200505 (2021)]. By bridging fault-tolerant computation and computational certification, logical accreditation offers a scalable, practical means of certifying the accuracy of quantum computations performed using encoded logical qubits.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Quantum computers have the potential to solve real-world problems that are intractable for classical computers, with proposed applications spanning the fields of materials science and quantum chemistry. Quantum error correction (QEC) is required to perform large-scale quantum computation; otherwise, errors quickly accumulate and computation fails. Recent experimental demonstrations of QEC mark a turning point on the path to large-scale quantum computing. However, the hardware constraints of near-term quantum devices limit error suppression, making it difficult to trust the accuracy of their outputs. Compounding this problem, many noise assumptions often used in QEC, including locality and Markovianity, may not be valid for real devices. There is an urgent need for practical tools to certify that quantum computations protected by QEC perform correctly under general, potentially highly correlated, device noise. To address this problem, we introduce logical accreditation, a scalable certification framework for quantum computations performed on qubits encoded with quantum error-correcting codes. Logical accreditation certifies the accuracy of quantum computations performed on encoded qubits and is robust to complex device noise that is potentially non-sparse and highly correlated. Crucially, it operates efficiently at scales where classical simulation methods fail and offers rigorous performance guarantees without relying on idealized noise models. We demonstrate the framework’s utility by certifying IQP and Hamiltonian simulation circuits with up to 500 logical qubits. Our framework enables experimentalists to verify that encoded quantum systems behave as intended and provides a practical tool to assess computational accuracy as devices scale toward fully fault-tolerant architectures.

Article Text

References (65)

  1. R. Acharya et al. (Google Quantum AI and Collaborators), Quantum error correction below the surface code threshold, Nature (London) 638, 920 (2025).
  2. 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. Bonilla Ataides, N. Maskara, I. Cong, X. Gao, P. Sales Rodriguez, T. Karolyshyn, G. Semeghini, M. J. Gullans, M. Greiner, V. Vuletić, and M. D. Lukin, Logical quantum processor based on reconfigurable atom arrays, Nature (London) 626, 58 (2024).
  3. A. Paetznick et al., Demonstration of logical qubits and repeated error correction with better-than-physical error rates, arXiv:2404.02280.
  4. A. Katabarwa, K. Gratsea, A. Caesura, and P. D. Johnson, Early fault-tolerant quantum computing, PRX Quantum 5, 020101 (2024).
  5. Y. Suzuki, S. Endo, K. Fujii, and Y. Tokunaga, Quantum error mitigation as a universal error reduction technique: Applications from the NISQ to the fault-tolerant quantum computing eras, PRX Quantum 3, 010345 (2022).
  6. A. Gheorghiu, T. Kapourniotis, and E. Kashefi, Verification of quantum computation: An overview of existing approaches, Theory Comput. Syst. 63, 715 (2019).
  7. E. Knill, D. Leibfried, R. Reichle, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, Randomized benchmarking of quantum gates, Phys. Rev. A 77, 012307 (2008).
  8. E. Magesan, J. M. Gambetta, and J. Emerson, Scalable and robust randomized benchmarking of quantum processes, Phys. Rev. Lett. 106, 180504 (2011).
  9. J. Helsen, I. Roth, E. Onorati, A. Werner, and J. Eisert, General framework for randomized benchmarking, PRX Quantum 3, 020357 (2022).
  10. A. W. Cross, L. S. Bishop, S. Sheldon, P. D. Nation, and J. M. Gambetta, Validating quantum computers using randomized model circuits, Phys. Rev. A 100, 032328 (2019).
  11. P. Jurcevic et al., Demonstration of quantum volume 64 on a superconducting quantum computing system, Quantum Sci. Technol. 6, 025020 (2021).
  12. E. Pelofske, A. Bärtschi, and S. Eidenbenz, Quantum volume in practice: What users can expect from NISQ devices, IEEE Trans. Quantum Eng. 3, 1 (2022).
  13. J. J. Wallman and J. Emerson, Noise tailoring for scalable quantum computation via randomized compiling, Phys. Rev. A 94, 052325 (2016).
  14. A. Hashim, R. K. Naik, A. Morvan, J.-L. Ville, B. Mitchell, J. M. Kreikebaum, M. Davis, E. Smith, C. Iancu, K. P. O’Brien, I. Hincks, J. J. Wallman, J. Emerson, and I. Siddiqi, Randomized compiling for scalable quantum computing on a noisy superconducting quantum processor, Phys. Rev. X 11, 041039 (2021).
  15. C. Piveteau, D. Sutter, S. Bravyi, J. M. Gambetta, and K. Temme, Error mitigation for universal gates on encoded qubits, Phys. Rev. Lett. 127, 200505 (2021).
  16. S. Ferracin, T. Kapourniotis, and A. Datta, Accrediting outputs of noisy intermediate-scale quantum computing devices, New J. Phys. 21, 113038 (2019).
  17. S. Ferracin, S. T. Merkel, D. McKay, and A. Datta, Experimental accreditation of outputs of noisy quantum computers, Phys. Rev. A 104, 042603 (2021).
  18. A. Jackson, T. Kapourniotis, and A. Datta, Accreditation of analogue quantum simulators, Proceed. Natl. Acad. Sci. 121, e2309627121 (2024).
  19. A. Jackson and A. Datta, Improved accreditation of analogue quantum simulation and establishing quantum advantage, arXiv:2502.06463.
  20. J. F. Fitzsimons and E. Kashefi, Unconditionally verifiable blind quantum computation, Phys. Rev. A 96, 012303 (2017).
  21. D. Leichtle, L. Music, E. Kashefi, and H. Ollivier, Verifying BQP computations on noisy devices with minimal overhead, PRX Quantum 2, 040302 (2021).
  22. T. Proctor, S. Seritan, E. Nielsen, K. Rudinger, K. Young, R. Blume-Kohout, and M. Sarovar, Establishing trust in quantum computations (2022).
  23. D. Stilck França and R. García-Patrón, Limitations of optimization algorithms on noisy quantum devices, Nat. Phys. 17, 1221 (2021).
  24. M. Demarty, J. Mills, K. Hammam, and R. Garcia-Patron, Entropy density benchmarking of near-term quantum circuits, arXiv:2412.18007.
  25. B. Eastin and E. Knill, Restrictions on transversal encoded quantum gate sets, Phys. Rev. Lett. 102, 110502 (2009).
  26. D. Horsman, A. G. Fowler, S. Devitt, and R. V. Meter, Surface code quantum computing by lattice surgery, New J. Phys. 14, 123011 (2012).
  27. Y. Akahoshi, K. Maruyama, H. Oshima, S. Sato, and K. Fujii, Partially fault-tolerant quantum computing architecture with error-corrected Clifford gates and space-time efficient analog rotations, PRX Quantum 5, 010337 (2024).
  28. Y. Akahoshi, R. Toshio, J. Fujisaki, H. Oshima, S. Sato, and K. Fujii, Compilation of trotter-based time evolution for partially fault-tolerant quantum computing architecture, PRX Quantum 6, 040319 (2025).
  29. D. Litinski, A game of surface codes: Large-scale quantum computing with lattice surgery, Quantum 3, 128 (2019).
  30. R. Toshio, Y. Akahoshi, J. Fujisaki, H. Oshima, S. Sato, and K. Fujii, Practical quantum advantage on partially fault-tolerant quantum computer, Phys. Rev. X 15, 021057 (2025).
  31. A. Erhard, H. Poulsen Nautrup, M. Meth, L. Postler, R. Stricker, M. Stadler, V. Negnevitsky, M. Ringbauer, P. Schindler, H. J. Briegel, R. Blatt, N. Friis, and T. Monz, Entangling logical qubits with lattice surgery, Nature (London) 589, 220 (2021).
  32. J. Zhang, Z.-Y. Chen, Y.-J. Wang, B.-H. Lu, H.-F. Zhang, J.-N. Li, P. Duan, Y.-C. Wu, and G.-P. Guo, Demonstrating a universal logical gate set in error-detecting surface codes on a superconducting quantum processor, npj Quantum Inf. 11, 177 (2025).
  33. A. Y. Kitaev, Quantum computations: Algorithms and error correction, Russ. Math. Surv. 52, 1191 (1997).
  34. A. Kitaev, A. Shen, and M. Vyalyi, Classical and Quantum Computation, Graduate Studies in Mathematics No. 47 (American Mathematical Society, Providence, 2002).
  35. M. Suzuki, General theory of fractal path integrals with applications to many-body theories and statistical physics, J. Math. Phys. 32, 400 (1991).
  36. D. W. Berry, G. Ahokas, R. Cleve, and B. C. Sanders, Efficient quantum algorithms for simulating sparse Hamiltonians, Commun. Math. Phys. 270, 359 (2007).
  37. D. Poulin, M. B. Hastings, D. Wecker, N. Wiebe, A. C. Doherty, and M. Troyer, The trotter step size required for accurate quantum simulation of quantum chemistry, Quantum Inf. Comput. 15, 361 (2015).
  38. S. Bravyi, M. Englbrecht, R. König, and N. Peard, Correcting coherent errors with surface codes, npj Quantum Inf. 4, 55 (2018).
  39. K. Tsubouchi, Y. Mitsuhashi, K. Sharma, and N. Yoshioka, Symmetric Clifford twirling for cost-optimal quantum error mitigation in early FTQC regime, npj Quantum Inf. 11, 104 (2025).
  40. D. Shepherd and M. J. Bremner, Temporally unstructured quantum computation, Proceed. R. Soc. A 465, 1413 (2009).
  41. M. J. Bremner, A. Montanaro, and D. J. Shepherd, Achieving quantum supremacy with sparse and noisy commuting quantum computations, Quantum 1, 8 (2017).
  42. D. Hangleiter, M. Kalinowski, D. Bluvstein, M. Cain, N. Maskara, X. Gao, A. Kubica, M. D. Lukin, and M. J. Gullans, Fault-tolerant compiling of classically hard IQP circuits on hypercubes, PRX Quantum 6, 020338 (2025).
  43. M. E. Beverland, P. Murali, M. Troyer, K. M. Svore, T. Hoefler, V. Kliuchnikov, G. H. Low, M. Soeken, A. Sundaram, and A. Vaschillo, Assessing requirements to scale to practical quantum advantage, arXiv:2211.07629.
  44. M. J. Bremner, A. Montanaro, and D. J. Shepherd, Average-case complexity versus approximate simulation of commuting quantum computations, Phys. Rev. Lett. 117, 080501 (2016).
  45. S. Bravyi and D. Gosset, Improved classical simulation of quantum circuits dominated by Clifford gates, Phys. Rev. Lett. 116, 250501 (2016).
  46. H. Pashayan, O. Reardon-Smith, K. Korzekwa, and S. D. Bartlett, Fast estimation of outcome probabilities for quantum circuits, PRX Quantum 3, 020361 (2022).
  47. R. Nandkishore and D. A. Huse, Many-body localization and thermalization in quantum statistical mechanics, Annu. Rev. Condens. Matter Phys. 6, 15 (2015).
  48. A. M. Childs, Y. Su, M. C. Tran, N. Wiebe, and S. Zhu, Theory of trotter error with commutator scaling, Phys. Rev. X 11, 011020 (2021).
  49. I. D. Kivlichan, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, W. Sun, Z. Jiang, N. Rubin, A. Fowler, A. Aspuru-Guzik, H. Neven, and R. Babbush, Improved fault-tolerant quantum simulation of condensed-phase correlated electrons via Trotterization, Quantum 4, 296 (2020).
  50. E. T. Campbell, Early fault-tolerant simulations of the Hubbard model, Quantum Sci. Technol. 7, 015007 (2022).
  51. M. Lostaglio and A. Ciani, Error mitigation and quantum-assisted simulation in the error corrected regime, Phys. Rev. Lett. 127, 200506 (2021).
  52. A. Dutkiewicz, S. Polla, M. Scheurer, C. Gogolin, W. J. Huggins, and T. E. O’Brien, Error mitigation and circuit division for early fault-tolerant quantum phase estimation, PRX Quantum 6, 040318 (2025).
  53. S. Endo, Z. Cai, S. C. Benjamin, and X. Yuan, Hybrid quantum-classical algorithms and quantum error mitigation, J. Phys. Soc. Jpn. 90, 032001 (2021).
  54. Z. Zimborás et al., Myths around quantum computation before full fault tolerance: What no-go theorems rule out and what they don’t, arXiv:2501.05694.
  55. S. Endo, S. C. Benjamin, and Y. Li, Practical quantum error mitigation for near-future applications, Phys. Rev. X 8, 031027 (2018).
  56. T. Schuster, C. Yin, X. Gao, and N. Y. Yao, A polynomial-time classical algorithm for noisy quantum circuits, Phys. Rev. X 15, 041018 (2025).
  57. R. Mezher, J. Mills, and E. Kashefi, Mitigating errors by quantum verification and postselection, Phys. Rev. A 105, 052608 (2022).
  58. J. Harris and E. Kashefi, Error mitigation of BQP computations using measurement-based verification, Phys. Rev. A 111, 022602 (2025).
  59. S. Bravyi and A. Kitaev, Universal quantum computation with ideal Clifford gates and noisy ancillas, Phys. Rev. A 71, 022316 (2005).
  60. E. T. Campbell, B. M. Terhal, and C. Vuillot, Roads towards fault-tolerant universal quantum computation, Nature (London) 549, 172 (2017).
  61. D. Litinski, Magic state distillation: Not as costly as you think, Quantum 3, 205 (2019).
  62. A. Winick, J. J. Wallman, D. Dahlen, I. Hincks, E. Ospadov, and J. Emerson, Concepts and conditions for error suppression through randomized compiling, arXiv:2212.07500.
  63. Z. Liu, Y. Xiao, and Z. Cai, Non-Markovian noise suppression simplified through channel representation, arXiv:2412.11220.
  64. P. Jordan and E. Wigner, Über das Paulische Äquivalenzverbot, Z. Phys. 47, 631 (1928).
  65. R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme, Simulating physical phenomena by quantum networks, Phys. Rev. A 65, 042323 (2002).

Outline

Information

PRX Quantum 7, 033053– Published 11 September, 2026
  • Received 8 October 2025
  • Revised 28 April 2026
  • Accepted 23 June 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