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  • Open Access

Toward extracting scattering phase shift from integrated correlation functions on quantum computers

Peng Guo*

  • *Contact author: peng.guo@dsu.edu
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Phys. Rev. Research 7, 043164 – Published 12 November, 2025

DOI: https://doi.org/10.1103/f9mm-vz8w

Abstract

Based on an established relation that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral, we propose to extract the infinite volume scattering phase shifts through quantum simulation of the integrated correlation functions of trapped two-particle systems on quantum computers. The integrated correlation function can be computed by an ancilla-based algorithm. The proposal is demonstrated with a simple contact interaction fermion model.

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References (61)

  1. S. Schaefer, R. Sommer, and F. Virotta (ALPHA Collaboration), Critical slowing down and error analysis in lattice QCD simulations, Nucl. Phys. B 845, 93 (2011).
  2. E. Y. Loh, J. E. Gubernatis, R. T. Scalettar, S. R. White, D. J. Scalapino, and R. L. Sugar, Sign problem in the numerical simulation of many-electron systems, Phys. Rev. B 41, 9301 (1990).
  3. P. de Forcrand, Simulating QCD at finite density, in Proceedings of the XXVII International Symposium on Lattice Field Theory (LAT2009) Beijing, P.R. China, July 26-31, 2009 (PoS LAT2009, Beijing, 2009).
  4. G. Peter Lepage, The analysis of algorithms for lattice field theory, in Proceedings of the Boulder Advanced Study Institute (ASI) (CERN, Boulder, CO, USA, 1989), pp. 97–120.
  5. C. Drischler, W. Haxton, K. McElvain, E. Mereghetti, A. Nicholson, P. Vranas, and A. Walker-Loud, Towards grounding nuclear physics in QCD, Prog. Part. Nucl. Phys. 121, 103888 (2021).
  6. M. Lüscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B 354, 531 (1991).
  7. T. Busch, B.-G. Englert, K. Rzażewski, and M. Wilkens, Two cold atoms in a harmonic trap, Found. Phys. 28, 549–559 (1998).
  8. K. Rummukainen and S. A. Gottlieb, Resonance scattering phase shifts on a nonrest frame lattice, Nucl. Phys. B 450, 397 (1995).
  9. N. H. Christ, C. Kim, and T. Yamazaki, Finite volume corrections to the two-particle decay of states with non-zero momentum, Phys. Rev. D 72, 114506 (2005).
  10. V. Bernard, M. Lage, U.-G. Meißner, and A. Rusetsky, Resonance properties from the finite-volume energy spectrum, J. High Energy Phys. 08 (2008) 024.
  11. S. He, X. Feng, and C. Liu, Two particle states and the s-matrix elements in multi-channel scattering, J. High Energy Phys. 07 (2005) 011.
  12. M. Lage, U.-G. Meißner, and A. Rusetsky, A method to measure the antikaon-nucleon scattering length in lattice QCD, Phys. Lett. B 681, 439 (2009).
  13. M. Döring, U.-G. Meißner, E. Oset, and A. Rusetsky, Unitarized chiral perturbation theory in a finite volume: Scalar meson sector, Eur. Phys. J. A 47, 139 (2011).
  14. P. Guo, J. Dudek, R. Edwards, and A. P. Szczepaniak, Coupled-channel scattering on a torus, Phys. Rev. D 88, 014501 (2013).
  15. P. Guo, Coupled-channel scattering in 1 + 1 dimensional lattice model, Phys. Rev. D 88, 014507 (2013).
  16. S. Kreuzer and H. W. Hammer, Efimov physics in a finite volume, Phys. Lett. B 673, 260 (2009).
  17. K. Polejaeva and A. Rusetsky, Three particles in a finite volume, Eur. Phys. J. A 48, 67 (2012).
  18. M. T. Hansen and S. R. Sharpe, Relativistic, model-independent, three-particle quantization condition, Phys. Rev. D 90, 116003 (2014).
  19. M. Mai and M. Döring, Three-body unitarity in the finite volume, Eur. Phys. J. A 53, 240 (2017).
  20. M. Mai and M. Döring, Finite-volume spectrum of π+π+ and π+π+π+ systems, Phys. Rev. Lett. 122, 062503 (2019).
  21. M. Döring, H. W. Hammer, M. Mai, J. Y Pang, A. Rusetsky, and J. Wu, Three-body spectrum in a finite volume: The role of cubic symmetry, Phys. Rev. D 97, 114508 (2018).
  22. P. Guo, One spatial dimensional finite volume three-body interaction for a short-range potential, Phys. Rev. D 95, 054508 (2017).
  23. P. Guo and V. Gasparian, A solvable three-body model in finite volume, Phys. Lett. B 774, 441 (2017).
  24. P. Guo and V. Gasparian, Numerical approach for finite volume three-body interaction, Phys. Rev. D 97, 014504 (2018).
  25. P. Guo and T. Morris, Multiple-particle interaction in (1 + 1)-dimensional lattice model, Phys. Rev. D 99, 014501 (2019).
  26. M. Mai, M. Döring, C. Culver, and A. Alexandru, Three-body unitarity versus finite-volume π+π+π+ spectrum from lattice QCD, Phys. Rev. D 101, 054510 (2020).
  27. P. Guo, M. Döring, and A. P. Szczepaniak, Variational approach to N-body interactions in finite volume, Phys. Rev. D 98, 094502 (2018).
  28. P. Guo, Propagation of particles on a torus, Phys. Lett. B 804, 135370 (2020).
  29. P. Guo and M. Döring, Lattice model of heavy-light three-body system, Phys. Rev. D 101, 034501 (2020).
  30. P. Guo, Threshold expansion formula of N bosons in a finite volume from a variational approach, Phys. Rev. D 101, 054512 (2020).
  31. P. Guo and B. Long, Multi- π+ systems in a finite volume, Phys. Rev. D 101, 094510 (2020).
  32. P. Guo, Myth of scattering in finite volume, arXiv:2007.04473 [hep-lat]
  33. P. Guo and B. Long, Visualizing resonances in finite volume, Phys. Rev. D 102, 074508 (2020).
  34. P. Guo, Modeling few-body resonances in finite volume, Phys. Rev. D 102, 054514 (2020).
  35. P. Guo and V. Gasparian, Charged particles interaction in both a finite volume and a uniform magnetic field, Phys. Rev. D 103, 094520 (2021).
  36. P. Guo and B. Long, Nuclear reactions in artificial traps, J. Phys. G: Nucl. Part. Phys. 49, 055104 (2022).
  37. P. Guo, Coulomb corrections to two-particle interactions in artificial traps, Phys. Rev. C 103, 064611 (2021).
  38. P. Guo and V. Gasparian, Charged particles interaction in both a finite volume and a uniform magnetic field II: Topological and analytic properties of a magnetic system, J. Phys. A 55, 265201 (2022).
  39. I. Stetcu, B. R. Barrett, U. van Kolck, and J. P. Vary, Effective theory for trapped few-fermion systems, Phys. Rev. A 76, 063613 (2007).
  40. I. Stetcu, J. Rotureau, B. R. Barrett, and U. van Kolck, An effective field theory approach to two trapped particles, Ann. Phys. 325, 1644 (2010).
  41. J. Rotureau, I. Stetcu, B. R. Barrett, M. C. Birse, and U. van Kolck, Three and four harmonically trapped particles in an effective field theory framework, Phys. Rev. A 82, 032711 (2010).
  42. J. Rotureau, I. Stetcu, B. R. Barrett, and U. van Kolck, Two and three nucleons in a trap and the continuum limit, Phys. Rev. C 85, 034003 (2012).
  43. T. Luu, M. J. Savage, A. Schwenk, and J. P. Vary, Nucleon-nucleon scattering in a harmonic potential, Phys. Rev. C 82, 034003 (2010).
  44. C.-J. Yang, Chiral potential renormalized in harmonic-oscillator space, Phys. Rev. C 94, 064004 (2016).
  45. C. W. Johnson et al., From bound states to the continuum, J. Phys. G: Nucl. Part. Phys. 47, 123001 (2020).
  46. X. Zhang, Extracting free-space observables from trapped interacting clusters, Phys. Rev. C 101, 051602 (2020).
  47. X. Zhang, S. R. Stroberg, P. Navrátil, C. Gwak, J. A. Melendez, R. J. Furnstahl, and J. D. Holt, Ab initio calculations of low-energy nuclear scattering using a generalized Lüscher method, Phys. Rev. Lett. 125, 112503 (2020).
  48. P. Wang, W. Du, W. Zuo, and J. P. Vary, Nuclear scattering via quantum computing, Phys. Rev. C 109, 064623 (2024).
  49. F. Turro, K. A. Wendt, S. Quaglioni, F. Pederiva, and A. Roggero, Evaluation of phase shifts for nonrelativistic elastic scattering using quantum computers, Phys. Rev. C 110, 054604 (2024).
  50. 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).
  51. G. Mussardo, A. Stampiggi, and A. Trombettoni, Reflection and transmission amplitudes in a digital quantum simulation, EPJ Quantum Technol. 11, 65 (2024).
  52. P. Guo and V. Gasparian, Toward extracting the scattering phase shift from integrated correlation functions, Phys. Rev. D 108, 074504 (2023).
  53. P. Guo, Toward extracting the scattering phase shift from integrated correlation functions. II. A relativistic lattice field theory model, Phys. Rev. D 110, 014504 (2024).
  54. P. Guo and F. X. Lee, Toward extracting scattering phase shift from integrated correlation functions. III. Coupled channels, Phys. Rev. D 111, 054506 (2025).
  55. G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme, Quantum algorithms for fermionic simulations, Phys. Rev. A 64, 022319 (2001).
  56. R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme, Simulating physical phenomena by quantum networks, Phys. Rev. A 65, 042323 (2002).
  57. P. Jordan and E. Wigner, Über das paulische äquivalenzverbot, Z. Phys. 47, 631 (1928).
  58. F. Tacchino, A. Chiesa, S. Carretta, and D. Gerace, Quantum computers as universal quantum simulators: State-of-the-art and perspectives, Adv. Quantum Technol. 3, 1900052 (2020).
  59. H. F. Trotter, On the product of semi-groups of operators, Proc. Am. Math. Soc. 10, 545 (1959).
  60. N. Hatano and M. Suzuki, Finding exponential product formulas of higher orders, Lect. Notes Phys. 679, 37 (2005).
  61. P. Guo, V. Gasparian, E. Jódar, and C. Wisehart, Tunneling time in PT-symmetric systems, Phys. Rev. A 107, 032210 (2023).

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Information

Phys. Rev. Research 7, 043164– Published 12 November, 2025
  • Received 22 April 2025
  • Accepted 22 October 2025
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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.

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