- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Quantum anomaly for benchmarking quantum computing

Tomoya Hayata

Arata Yamamoto

PDF

Phys. Rev. Research 8, 033349 – Published 22 September, 2026

DOI: https://doi.org/10.1103/l8w6-pk4m

Abstract

Given the rapid advances in quantum computing hardware, establishing strategies for verifying the correctness of quantum computations has become increasingly important. Exploiting the fact that the axial anomaly in gauge theories is exact to all orders in perturbation theory, we propose the axial anomaly as a nontrivial benchmark for quantum simulations of lattice gauge theories. We simulate axial charge production in ZN lattice gauge theories on the trapped-ion quantum computer “Reimei.” After taking the U(1), infinitesimal time, and infinite volume limits, we successfully reproduce the anomaly coefficient within statistical uncertainties, even without error mitigation. Our results demonstrate that the axial anomaly can be simulated on current quantum computers and serves as a verification test of quantum computations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (32)

  1. N. Klco, J. R. Stryker, and M. J. Savage, SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers, Phys. Rev. D 101, 074512 (2020).
  2. A. Yamamoto, Real-time simulation of (2+1)-dimensional lattice gauge theory on qubits, Prog. Theor. Exp. Phys. 2021, 013B06 (2021).
  3. N. H. Nguyen, M. C. Tran, Y. Zhu, A. M. Green, C. H. Alderete, Z. Davoudi, and N. M. Linke, Digital quantum simulation of the Schwinger model and symmetry protection with trapped ions, PRX Quantum 3, 020324 (2022).
  4. J. Mildenberger, W. Mruczkiewicz, J. C. Halimeh, Z. Jiang, and P. Hauke, Confinement in a Z2 lattice gauge theory on a quantum computer, Nat. Phys. 21, 312 (2025).
  5. S. A Rahman, R. Lewis, E. Mendicelli, and S. Powell, Self-mitigating Trotter circuits for SU(2) lattice gauge theory on a quantum computer, Phys. Rev. D 106, 074502 (2022).
  6. Y. Y. Atas, J. F. Haase, J. Zhang, V. Wei, S. M. L. Pfaendler, R. Lewis, and C. A. Muschik, Simulating one-dimensional quantum chromodynamics on a quantum computer: Real-time evolutions of tetra- and pentaquarks, Phys. Rev. Res. 5, 033184 (2023).
  7. D. Pomarico, L. Cosmai, P. Facchi, C. Lupo, S. Pascazio, and F. V. Pepe, Dynamical quantum phase transitions of the Schwinger model: Real-time dynamics on IBM Quantum, Entropy 25, 608 (2023).
  8. C. Charles, E. J. Gustafson, E. Hardt, F. Herren, N. Hogan, H. Lamm, S. Starecheski, R. S. Van de Water, and M. L. Wagman, Simulating Z2 lattice gauge theory on a quantum computer, Phys. Rev. E 109, 015307 (2024).
  9. T. Angelides, P. Naredi, A. Crippa, K. Jansen, S. Kühn, I. Tavernelli, and D. S. Wang, First-order phase transition of the Schwinger model with a quantum computer, npj Quantum Inf. 11, 6 (2025).
  10. T. A. Cochran et al., Visualizing dynamics of charges and strings in (2+1)D lattice gauge theories, Nature (London) 642, 315 (2025).
  11. Z. Davoudi, C.-C. Hsieh, and S. V. Kadam, Quantum computation of hadron scattering in a lattice gauge theory, arXiv:2505.20408 [quant-ph].
  12. E. O. Rosanowski, A. Crippa, L. Funcke, P. V. Itaborai, K. Jansen, and S. Singh, (2+1)D quantum electrodynamics at finite density on a quantum computer, Phys. Rev. D 114, 014501 (2026).
  13. T. Hayata, Y. Hidaka, and Y. Kikuchi, Onset of thermalization of q-deformed SU(2) Yang-Mills theory on a trapped-ion quantum computer Phys. Rev. Res. 8, 033137 (2026).
  14. R. C. Farrell, M. Illa, A. N. Ciavarella, and M. J. Savage, Scalable circuits for preparing ground states on digital quantum computers: The Schwinger model vacuum on 100 qubits, PRX Quantum 5, 020315 (2024).
  15. R. C. Farrell, M. Illa, A. N. Ciavarella, and M. J. Savage, Quantum simulations of hadron dynamics in the Schwinger model using 112 qubits, Phys. Rev. D 109, 114510 (2024).
  16. T. Hayata, K. Seki, and A. Yamamoto, Floquet prethermalization of Z2 lattice gauge theory on superconducting qubits, Phys. Rev. D 110, 114503 (2024).
  17. T. Hayata and Y. Hidaka, Floquet evolution of the q-deformed SU(3)1 Yang-Mills theory on a two-leg ladder, Phys. Rev. D 111, 034513 (2025).
  18. E. Abdalla, M. C. B. Abdalla, and K. D. Rothe, Nonperturbative Methods in Two-Dimensional Quantum Field Theory (World Scientific, Singapore, 1991).
  19. H. B. Nielsen and M. Ninomiya, No go theorem for regularizing chiral fermions, Phys. Lett. B 105, 219 (1981).
  20. M. Creutz, I. Horvath, and H. Neuberger, A new fermion Hamiltonian for lattice gauge theory, Nucl. Phys. B Proc. Suppl. 106-107, 760 (2002).
  21. K. Matsui, T. Okamoto, and T. Fujiwara, Canonical approach to Ginsparg-Wilson fermion, Phys. Rev. D 71, 114501 (2005).
  22. T. Hayata, K. Nakayama, and A. Yamamoto, Chiral fermion in the Hamiltonian lattice gauge theory, Phys. Rev. D 108, 034511 (2023).
  23. A. Chatterjee, S. D. Pace, and S.-H. Shao, Quantized axial charge of staggered fermions and the chiral anomaly, Phys. Rev. Lett. 134, 021601 (2025).
  24. Y. Hidaka and A. Yamamoto, Anomaly of conserved and nonconserved axial charges in Hamiltonian lattice gauge theory, Prog. Theor. Exp. Phys. 2025, 093B04 (2025).
  25. T. Onogi and T. Yamaoka, Non-singlet conserved charges and anomalies in 3+1 D staggered fermions, arXiv:2509.04906 [hep-lat].
  26. S. Aoki, Y. Kikukawa, and T. Takemoto, Chiral anomaly of Kogut-Susskind fermions in the (3+1)-dimensional Hamiltonian formalism, Phys. Rev. D 113, 034514 (2026).
  27. T. Hayata, K. Nakayama, and A. Yamamoto, Dynamical chirality production in one dimension, Phys. Rev. D 109, 034501 (2024).
  28. H. Singh, Ginsparg-Wilson Hamiltonians with improved chiral symmetry, arXiv:2505.20419 [hep-lat].
  29. D. Horn, M. Weinstein, and S. Yankielowicz, Hamiltonian approach to Z(N) lattice gauge theories, Phys. Rev. D 19, 3715 (1979).
  30. D. Wecker, M. B. Hastings, N. Wiebe, B. K. Clark, C. Nayak, and M. Troyer, Solving strongly correlated electron models on a quantum computer, Phys. Rev. A 92, 062318 (2015).
  31. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2012).
  32. S. Sivarajah, S. Dilkes, A. Cowtan, W. Simmons, A. Edgington, and R. Duncan, t|ket〉: a retargetable compiler for NISQ devices, Quantum Sci. Technol. 6, 014003 (2021).

Outline

Information

Phys. Rev. Research 8, 033349– Published 22 September, 2026
  • Received 6 March 2026
  • Accepted 5 September 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