- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

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
  • Letter
  • Open Access

Real-time estimators for scattering observables: A full account of finite-volume errors for quantum simulation

Ivan M. Burbano1,2,3,*, Marco A. Carrillo4,5,†, Rana Urek1,2,‡, Anthony N. Ciavarella3,§, and Raúl A. Briceño1,2,∥

  • *Contact author: ivan_burbano@berkeley.edu
  • †Contact author: mcarr020@odu.edu
  • ‡Contact author: urek@berkeley.edu
  • §Contact author: anciavarella@lbl.gov
  • ∥Contact author: rbriceno@berkeley.edu
PDF

Phys. Rev. D 113, L071502 – Published 9 April, 2026

DOI: https://doi.org/10.1103/dc17-4zjy

Abstract

The real-time correlators of quantum field theories can be directly probed through new approaches to simulation, such as quantum computing and tensor networks. This provides a new framework for computing scattering observables in lattice formulations of strongly interacting theories, such as lattice quantum chromodynamics. In this paper, we prove that the proposal of real-time estimators of scattering observables is universally applicable to all scattering observables of gapped quantum field theories. All finite-volume errors are exponentially suppressed, and the rate of this suppression is controlled by the regulator considered, namely, a displacement of the spectrum of the theory into the complex plane. A partial restoration of Lorentz symmetry by averaging over different boosts gives an additional suppression of finite volume errors. Our results also apply to the simulation of wave packet scattering, where a similar averaging is performed to construct the wave packets that regulate the finite volume effects. This result represents a necessary key step toward determining a broad class of scattering observables via quantum computing that are currently inaccessible via classical computing. Such observables are relevant for various applications, including hadron spectroscopy, hadron structure, and precision tests of the Standard Model. We also comment on potential applications of our results to traditional computational schemes.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (94)

  1. R. Acciarri et al. (DUNE Collaboration), Long-baseline neutrino facility (LBNF) and deep underground neutrino experiment (DUNE): Conceptual design report, volume 1: The LBNF and DUNE projects, arXiv:1601.05471.
  2. B. Abi et al. (DUNE Collaboration), Prospects for beyond the standard model physics searches at the deep underground neutrino experiment, Eur. Phys. J. C 81, 322 (2021).
  3. A. Accardi et al., Electron ion collider: The next QCD frontier: Understanding the glue that binds us all, Eur. Phys. J. A 52, 268 (2016).
  4. R. Abdul Khalek et al., Snowmass 2021 white paper: Electron ion collider for high energy physics, arXiv:2203.13199.
  5. M. Luscher, Volume dependence of the energy spectrum in massive quantum field theories. I. Stable particle states, Commun. Math. Phys. 104, 177 (1986).
  6. M. Luscher, Volume dependence of the energy spectrum in massive quantum field theories. II. Scattering states, Commun. Math. Phys. 105, 153 (1986).
  7. M. Luscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B354, 531 (1991).
  8. R. A. Briceno, J. J. Dudek, and R. D. Young, Scattering processes and resonances from lattice QCD, Rev. Mod. Phys. 90, 025001 (2018).
  9. M. T. Hansen and S. R. Sharpe, Lattice QCD and three-particle decays of resonances, Annu. Rev. Nucl. Part. Sci. 69, 65 (2019).
  10. M. Mai, M. Döring, and A. Rusetsky, Multi-particle systems on the lattice and chiral extrapolations: A brief review, Eur. Phys. J. Spec. Top. 230, 1623 (2021).
  11. J. Bulava et al., Hadron spectroscopy with lattice QCD, in Snowmass 2021 (2022), arXiv:2203.03230.

  12. Which happens when the energy of the system is equal to or greater than the sum of the masses of the three particles.

  13. S. M. Dawid, Z. T. Draper, A. D. Hanlon, B. Hörz, C. Morningstar, F. Romero-López, S. R. Sharpe, and S. Skinner, QCD predictions for physical multimeson scattering amplitudes, Phys. Rev. Lett. 135, 021903 (2025).
  14. A. W. Jackura, Three-body scattering and quantization conditions from S-matrix unitarity, Phys. Rev. D 108, 034505 (2023).
  15. M. T. Hansen, R. A. Briceño, R. G. Edwards, C. E. Thomas, and D. J. Wilson (Hadron Spectrum Collaboration), Energy-dependent π+π+π+ scattering amplitude from QCD, Phys. Rev. Lett. 126, 012001 (2021).
  16. R. A. Briceño, C. S. R. Costa, and A. W. Jackura, Partial-wave projection of relativistic three-body amplitudes, Phys. Rev. D 111, 036029 (2025).
  17. M. Mai and M. Doring, Finite-volume spectrum of π+π+ and π+π+π+ systems, Phys. Rev. Lett. 122, 062503 (2019).
  18. M. Mai and M. Döring, Three-body unitarity in the finite volume, Eur. Phys. J. A 53, 240 (2017).
  19. S. P. Jordan, H. Krovi, K. S. M. Lee, and J. Preskill, BQP-completeness of scattering in scalar quantum field theory, Quantum 2, 44 (2018).
  20. R. A. Briceño, J. V. Guerrero, M. T. Hansen, and A. M. Sturzu, Role of boundary conditions in quantum computations of scattering observables, Phys. Rev. D 103, 014506 (2021).
  21. R. A. Briceño, M. A. Carrillo, J. V. Guerrero, M. T. Hansen, and A. M. Sturzu, Accessing scattering amplitudes using quantum computers, Proc. Sci. LATTICE2021 (2022) 315 [arXiv:2112.01968].
  22. M. A. Carrillo, R. A. Briceño, and A. M. Sturzu, Inclusive reactions from finite Minkowski spacetime correlation functions, Phys. Rev. D 110, 054503 (2024).
  23. I. Raychowdhury and J. R. Stryker, Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories, Phys. Rev. D 101, 114502 (2020).
  24. S. V. Kadam, I. Raychowdhury, and J. R. Stryker, Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks, Phys. Rev. D 107, 094513 (2023).
  25. S. V. Kadam, A. Naskar, I. Raychowdhury, and J. R. Stryker, Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: Hilbert space of a trivalent vertex, Phys. Rev. D 111, 074516 (2025).
  26. A. Ciavarella, N. Klco, and M. J. Savage, Trailhead for quantum simulation of SU(3) Yang-Mills lattice gauge theory in the local multiplet basis, Phys. Rev. D 103, 094501 (2021).
  27. I. D’Andrea, C. W. Bauer, D. M. Grabowska, and M. Freytsis, New basis for Hamiltonian SU(2) simulations, Phys. Rev. D 109, 074501 (2024).
  28. D. M. Grabowska, C. F. Kane, and C. W. Bauer, Fully gauge-fixed SU(2) Hamiltonian for quantum simulations, Phys. Rev. D 111, 114516 (2025).
  29. I. M. Burbano and C. W. Bauer, Gauge loop-string-hadron formulation on general graphs and applications to fully gauge fixed Hamiltonian lattice gauge theory, J. High Energy Phys. 12 (2025) 060.
  30. G. Bergner, M. Hanada, E. Rinaldi, and A. Schafer, Toward QCD on quantum computer: Orbifold lattice approach, J. High Energy Phys. 05 (2024) 234.
  31. A. N. Ciavarella and C. W. Bauer, Quantum simulation of SU(3) lattice Yang-Mills theory at leading order in large-Nc expansion, Phys. Rev. Lett. 133, 111901 (2024).
  32. A. N. Ciavarella, I. M. Burbano, and C. W. Bauer, Efficient truncations of SU(Nc) lattice gauge theory for quantum simulation, Phys. Rev. D 112, 054514 (2025).
  33. B. Assi and H. Lamm, Digitization and subduction of SU(N) gauge theories, Phys. Rev. D 110, 074511 (2024).
  34. 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).
  35. E. R. Bennewitz et al., Simulating meson scattering on spin quantum simulators, Quantum 9, 1773 (2025).
  36. Z. Davoudi, C.-C. Hsieh, and S. V. Kadam, Quantum computation of hadron scattering in a lattice gauge theory, arXiv:2505.20408.
  37. J. Schuhmacher, G.-X. Su, J. J. Osborne, A. Gandon, J. C. Halimeh, and I. Tavernelli, Observation of hadron scattering in a lattice gauge theory on a quantum computer, arXiv:2505.20387.
  38. R. C. Farrell, N. A. Zemlevskiy, M. Illa, and J. Preskill, Digital quantum simulations of scattering in quantum field theories using W states, arXiv:2505.03111.
  39. J. Ingoldby, M. Spannowsky, T. Sypchenko, S. Williams, and M. Wingate, Real-time scattering on quantum computers via Hamiltonian truncation, arXiv:2505.03878.
  40. M. Yusf, L. Gan, C. Moffat, and G. Rupak, Elastic scattering on a quantum computer, Phys. Rev. C 111, 034001 (2025).
  41. Y. Chai, Y. Guo, and S. Kühn, Towards quantum simulation of meson scattering in a Z2 lattice gauge theory, arXiv:2505.21240.
  42. S. Abel, M. Spannowsky, and S. Williams, Real-time scattering processes with continuous-variable quantum computers, Phys. Rev. A 112, 012614 (2025).
  43. S. Sharma, T. Papenbrock, and L. Platter, Scattering phase shifts from a quantum computer, Phys. Rev. C 109, L061001 (2024).
  44. S. Wu, W. Du, X. Zhao, and J. P. Vary, Efficient and precise quantum simulation of ultrarelativistic quark-nucleus scattering, Phys. Rev. D 110, 056044 (2024).
  45. A. Rajput, A. Roggero, and N. Wiebe, Quantum error correction with gauge symmetries, npj Quantum Inf. 9, 41 (2023).
  46. X. Yao, Quantum error correction codes for truncated SU(2) lattice gauge theories, arXiv:2511.13721.
  47. J. C. Halimeh, H. Lang, and P. Hauke, Gauge protection in non-Abelian lattice gauge theories, New J. Phys. 24, 033015 (2022).
  48. J. C. Halimeh, L. Homeier, C. Schweizer, M. Aidelsburger, P. Hauke, and F. Grusdt, Stabilizing lattice gauge theories through simplified local pseudogenerators, Phys. Rev. Res. 4, 033120 (2022).
  49. Y.-A. Chen, A. V. Gorshkov, and Y. Xu, Error-correcting codes for fermionic quantum simulation, SciPost Phys. 16, 033 (2024).
  50. J. R. Stryker, Oracles for Gauss’s law on digital quantum computers, Phys. Rev. A 99, 042301 (2019).
  51. L. Spagnoli, A. Roggero, and N. Wiebe, Fault-tolerant simulation of lattice gauge theories with gauge covariant codes, Quantum 10, 1968 (2026).
  52. M. Carena, H. Lamm, Y.-Y. Li, and W. Liu, Quantum error thresholds for gauge-redundant digitizations of lattice field theories, Phys. Rev. D 110, 054516 (2024).
  53. P. Faist, S. Nezami, V. V. Albert, G. Salton, F. Pastawski, P. Hayden, and J. Preskill, Continuous symmetries and approximate quantum error correction, Phys. Rev. X 10, 041018 (2020).
  54. J. C. Halimeh, N. Mueller, J. Knolle, Z. Papić, and Z. Davoudi, Quantum simulation of out-of-equilibrium dynamics in gauge theories, arXiv:2509.03586.
  55. Z. Davoudi, TASI/CERN/KITP lecture notes on “toward quantum computing gauge theories of nature,” arXiv:2507.15840.
  56. C. W. Bauer, Efficient use of quantum computers for collider physics, J. High Energy Phys. 11 (2025) 108.
  57. A. Di Meglio et al., Quantum computing for high-energy physics: State of the art and challenges, PRX Quantum 5, 037001 (2024).
  58. C. W. Bauer et al., Quantum simulation for high-energy physics, PRX Quantum 4, 027001 (2023).
  59. Z. Davoudi et al., Report of the snowmass 2021 topical group on lattice gauge theory, in Snowmass 2021 (2022), arXiv:2209.10758.
  60. S. Catterall et al., Report of the snowmass 2021 theory frontier topical group on quantum information science, in Snowmass 2021 (2022), arXiv:2209.14839.
  61. S. P. Jordan, K. S. M. Lee, and J. Preskill, Quantum algorithms for quantum field theories, Science 336, 1130 (2012).
  62. S. P. Jordan, K. S. M. Lee, and J. Preskill, Quantum computation of scattering in scalar quantum field theories, Quantum Inf. Comput. 14, 1014 (2014).
  63. S. P. Jordan, K. S. M. Lee, and J. Preskill, Quantum algorithms for fermionic quantum field theories, arXiv:1404.7115.
  64. R. G. Jha, A. Milsted, D. Neuenfeld, J. Preskill, and P. Vieira, Real-time scattering in ising field theory using matrix product states, Phys. Rev. Res. 7, 023266 (2025).
  65. E. Gustafson, Y. Meurice, and J. Unmuth-Yockey, Quantum simulation of scattering in the quantum Ising model, Phys. Rev. D 99, 094503 (2019).
  66. E. Gustafson, Y. Zhu, P. Dreher, N. M. Linke, and Y. Meurice, Real-time quantum calculations of phase shifts using wave packet time delays, Phys. Rev. D 104, 054507 (2021).
  67. Z. Parks, A. Carignan-Dugas, E. Gustafson, Y. Meurice, and P. Dreher, Applying the noiseless extrapolation error mitigation protocol to calculate real-time quantum field theory scattering phase shifts, Phys. Rev. D 109, 014505 (2024).
  68. A. Ciavarella, Algorithm for quantum computation of particle decays, Phys. Rev. D 102, 094505 (2020).
  69. R. A. Briceño, R. G. Edwards, M. Eaton, C. González-Arciniegas, O. Pfister, and G. Siopsis, Toward coherent quantum computation of scattering amplitudes with a measurement-based photonic quantum processor, Phys. Rev. Res. 6, 043065 (2024).
  70. T. Iadecola, S. Sen, and L. Sivertsen, Floquet insulators and lattice fermions, Phys. Rev. Lett. 132, 136601 (2024).
  71. Y. Chai, A. Crippa, K. Jansen, S. Kühn, V. R. Pascuzzi, F. Tacchino, and I. Tavernelli, Fermionic wave packet scattering: A quantum computing approach, Quantum 9, 1638 (2025).
  72. 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).
  73. 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).
  74. A. N. Ciavarella, String breaking in the heavy quark limit with scalable circuits, Phys. Rev. D 111, 054501 (2025).
  75. R. C. Farrell, M. Illa, and M. J. Savage, Steps toward quantum simulations of hadronization and energy loss in dense matter, Phys. Rev. C 111, 015202 (2025).
  76. E. Gustafson et al., Surrogate constructed scalable circuits ADAPT-VQE in the Schwinger model, Phys. Rev. Appl. 23, 064002 (2025).
  77. Z. Davoudi, C.-C. Hsieh, and S. V. Kadam, Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer, Quantum 8, 1520 (2024).
  78. J. Liu, Z. Li, H. Zheng, X. Yuan, and J. Sun, Towards a variational Jordan–Lee–Preskill quantum algorithm, Mach. Learn. Sci. Tech. 3, 045030 (2022).
  79. N. A. Zemlevskiy, Scalable quantum simulations of scattering in scalar field theory on 120 qubits, Phys. Rev. D 112, 034502 (2025).
  80. J. S. Pedernales, R. Di Candia, I. L. Egusquiza, J. Casanova, and E. Solano, Efficient quantum algorithm for computing n-time correlation functions, Phys. Rev. Lett. 113, 020505 (2014).
  81. X. Wang, L. Xiong, X. Cai, and X. Yuan, Computing n-time correlation functions without ancilla qubits, Phys. Rev. Lett. 135, 230602 (2025).
  82. R. C. Farrell, I. A. Chernyshev, S. J. M. Powell, N. A. Zemlevskiy, M. Illa, and M. J. Savage, Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. II. Single-baryon β-decay in real time, Phys. Rev. D 107, 054513 (2023).

  83. Given our interest in finite-volume artifacts, we will not discuss ultraviolet (UV) divergences in this work. Since both finite-volume and infinite-volume diagrams share the same UV structure, finite-volume corrections are UV finite.

  84. S. Coleman, Lectures of Sidney Coleman on Quantum Field Theory, edited by B. G.-g. Chen, D. Derbes, D. Griffiths, B. Hill, R. Sohn, and Y.-S. Ting (WSP, Hackensack, 2018).
  85. S. Weinzierl, Feynman Integrals. A Comprehensive Treatment for Students and Researchers, UNITEXT for Physics (Springer, New York, 2022).

  86. The reader might find it useful to note that gΔ is the second Symanzik polynomial.

  87. Z. Davoudi and S. V. Kadam, Two-neutrino double-β decay in pionless effective field theory from a Euclidean finite-volume correlation function, Phys. Rev. D 102, 114521 (2020).
  88. A. Baroni, R. A. Briceño, M. T. Hansen, and F. G. Ortega-Gama, Form factors of two-hadron states from a covariant finite-volume formalism, Phys. Rev. D 100, 034511 (2019).
  89. R. A. Briceño and M. T. Hansen, Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume, Phys. Rev. D 94, 013008 (2016).
  90. R. A. Briceno and Z. Davoudi, Moving multichannel systems in a finite volume with application to proton-proton fusion, Phys. Rev. D 88, 094507 (2013).
  91. J. Lozano, U.-G. Meißner, F. Romero-López, A. Rusetsky, and G. Schierholz, Resonance form factors from finite-volume correlation functions with the external field method, J. High Energy Phys. 10 (2022) 106.
  92. S. Mizera and S. Telen, Landau discriminants, J. High Energy Phys. 08 (2022) 200.
  93. R. A. Briceno, Z. Davoudi, T. C. Luu, and M. J. Savage, Two-baryon systems with twisted boundary conditions, Phys. Rev. D 89, 074509 (2014).
  94. C. h. Kim, C. T. Sachrajda, and S. R. Sharpe, Finite-volume effects for two-hadron states in moving frames, Nucl. Phys. B727, 218 (2005).

Outline

Information

Phys. Rev. D 113, L071502– Published 9 April, 2026
  • Received 20 June 2025
  • Accepted 13 March 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. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation