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JIMWLK on a quantum computer

Anjali A. Agrawal*, Evan Budd†, Alexander F. Kemper‡, and Vladimir V. Skokov§

Andrey Tarasov∥

Shaswat Tiwari

  • *Contact author: aaagraw2@ncsu.edu
  • †Contact author: embudd@ncsu.edu
  • ‡Contact author: akemper@ncsu.edu
  • §Contact author: vskokov@ncsu.edu
  • ∥Contact author: ataraso@ncsu.edu
  • Contact author: sstiwari@ncsu.edu
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Phys. Rev. D 113, 114047 – Published 25 June, 2026

DOI: https://doi.org/10.1103/d8tc-jkmk

Abstract

We propose a method for solving the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution equation on quantum computers. Our approach exploits the reformulation of the JIMWLK equation as a Lindblad master equation governing the rapidity evolution of the hadronic density matrix, as established in prior work. To render the problem tractable for quantum simulation, we introduce several approximations: the two-dimensional transverse plane is reduced to a one-dimensional radial lattice by assuming azimuthal symmetry of the jump operators; the gauge group is restricted to SU(2); and the infinite Wilson lines of the JIMWLK equation are replaced by finite Wilson links along the light-cone direction. The resulting bosonic Hilbert space is truncated using the electric field basis familiar from Hamiltonian lattice gauge theory, with states restricted to angular momenta j≤jmax. We derive the matrix elements of the JIMWLK Lindblad jump operators in this basis. As a benchmark, we demonstrate rapid convergence of the fundamental dipole expectation value with jmax for both pure and mixed Gaussian initial density matrices. For the simplest truncation, jmax=1/2, we implement the Lindblad evolution using a quantum simulation algorithm verified with the Qiskit statevector simulator by decomposing the non-unitary evolution operator into a linear combination of unitaries. This work establishes a concrete pathway toward quantum simulation of high-energy quantum chromodynamics evolution equations, with direct relevance to the physics program of the Electron-Ion Collider.

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References (82)

  1. J. Jalilian-Marian, A. Kovner, A. Leonidov, and H. Weigert, The BFKL equation from the Wilson renormalization group, Nucl. Phys. B504, 415 (1997).
  2. J. Jalilian-Marian, A. Kovner, and H. Weigert, The Wilson renormalization group for low x physics: Gluon evolution at finite parton density, Phys. Rev. D 59, 014015 (1998).
  3. J. Jalilian-Marian, A. Kovner, A. Leonidov, and H. Weigert, The Wilson renormalization group for low x physics: Towards the high density regime, Phys. Rev. D 59, 014014 (1998).
  4. A. Kovner, J. G. Milhano, and H. Weigert, Relating different approaches to nonlinear QCD evolution at finite gluon density, Phys. Rev. D 62, 114005 (2000).
  5. A. Kovner and J. G. Milhano, Vector potential versus color charge density in low x evolution, Phys. Rev. D 61, 014012 (2000).
  6. E. Iancu, A. Leonidov, and L. D. McLerran, Nonlinear gluon evolution in the color glass condensate. 1, Nucl. Phys. A692, 583 (2001).
  7. E. Iancu, A. Leonidov, and L. D. McLerran, The renormalization group equation for the color glass condensate, Phys. Lett. B 510, 133 (2001).
  8. E. Ferreiro, E. Iancu, A. Leonidov, and L. McLerran, Nonlinear gluon evolution in the color glass condensate. 2, Nucl. Phys. A703, 489 (2002).
  9. H. Weigert, Unitarity at small Bjorken x, Nucl. Phys. A703, 823 (2002).
  10. 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).
  11. R. Abdul Khalek et al., Science requirements and detector concepts for the electron-ion collider: EIC yellow report, Nucl. Phys. A1026, 122447 (2022).
  12. J.-P. Blaizot, E. Iancu, and H. Weigert, Nonlinear gluon evolution in path integral form, Nucl. Phys. A713, 441 (2003).
  13. T. Lappi and H. Mäntysaari, On the running coupling in the JIMWLK equation, Eur. Phys. J. C 73, 2307 (2013).
  14. A. Kovner, M. Lublinsky, and Y. Mulian, NLO JIMWLK evolution unabridged, J. High Energy Phys. 08 (2014) 114.
  15. A. Kovner, M. Lublinsky, and Y. Mulian, Conformal symmetry of JIMWLK evolution at NLO, J. High Energy Phys. 04 (2014) 030.
  16. M. Lublinsky and Y. Mulian, High Energy QCD at NLO: From light-cone wave function to JIMWLK evolution, J. High Energy Phys. 05 (2017) 097.
  17. T. Altinoluk, G. Beuf, M. Lublinsky, and V. V. Skokov, On running coupling in the JIMWLK evolution and its Langevin formulation, J. High Energy Phys. 03 (2024) 131.
  18. F. Cougoulic and Y. V. Kovchegov, Helicity-dependent generalization of the JIMWLK evolution, Phys. Rev. D 100, 114020 (2019).
  19. A. Kovner and M. Lublinsky, One gluon, two gluon: Multigluon production via high energy evolution, J. High Energy Phys. 11 (2006) 083.
  20. E. Iancu and D. N. Triantafyllopoulos, JIMWLK evolution for multi-particle production in Langevin form, J. High Energy Phys. 11 (2013) 067.
  21. N. Armesto, F. Dominguez, A. Kovner, M. Lublinsky, and V. Skokov, The color glass condensate density matrix: Lindblad evolution, entanglement entropy and Wigner functional, J. High Energy Phys. 05 (2019) 025.
  22. M. Li and A. Kovner, JIMWLK evolution, Lindblad equation and quantum-classical correspondence, J. High Energy Phys. 05 (2020) 036.
  23. G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119 (1976).
  24. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N level systems, J. Math. Phys. (N.Y.) 17, 821 (1976).
  25. J. Dalibard, Y. Castin, and K. Molmer, Wave-function approach to dissipative processes in quantum optics, Phys. Rev. Lett. 68, 580 (1992).
  26. W. H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys. 75, 715 (2003).
  27. Y. Akamatsu, Heavy quark master equations in the Lindblad form at high temperatures, Phys. Rev. D 91, 056002 (2015).
  28. N. Brambilla, M. A. Escobedo, J. Soto, and A. Vairo, Quarkonium suppression in heavy-ion collisions: An open quantum system approach, Phys. Rev. D 96, 034021 (2017).
  29. D. De Boni, Fate of in-medium heavy quarks via a Lindblad equation, J. High Energy Phys. 08 (2017) 064.
  30. J.-P. Blaizot and M. A. Escobedo, Quantum and classical dynamics of heavy quarks in a quark-gluon plasma, J. High Energy Phys. 06 (2018) 034.
  31. N. Mueller, A. Tarasov, and R. Venugopalan, Deeply inelastic scattering structure functions on a hybrid quantum computer, Phys. Rev. D 102, 016007 (2020).
  32. J. Barata, N. Mueller, A. Tarasov, and R. Venugopalan, Single-particle digitization strategy for quantum computation of a ϕ4 scalar field theory, Phys. Rev. A 103, 042410 (2021).
  33. G. Chachamis, M. Hentschinski, and A. Sabio Vera, Von Neumann entropy and Lindblad decoherence in the high-energy limit of strong interactions, Phys. Rev. D 109, 054015 (2024).
  34. 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).
  35. M. C. Bañuls et al., Simulating lattice gauge theories within quantum technologies, Eur. Phys. J. D 74, 165 (2020).
  36. C. W. Bauer et al., Quantum simulation for high-energy physics, PRX Quantum 4, 027001 (2023).
  37. E. Zohar, Quantum simulation of lattice gauge theories in more than one space dimension—requirements, challenges and methods, Phil. Trans. R. Soc. A 380, 20210069 (2021).
  38. Z. Davoudi, C.-C. Hsieh, and S. V. Kadam, Quantum computation of hadron scattering in a lattice gauge theory, arXiv:2505.20408.
  39. 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).
  40. 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).
  41. A. Ciavarella, N. Klco, and M. J. Savage, Some conceptual aspects of operator design for quantum simulations of non-Abelian lattice gauge theories, arXiv:2203.11988.
  42. Y. Y. Atas, J. Zhang, R. Lewis, A. Jahanpour, J. F. Haase, and C. A. Muschik, SU(2) hadrons on a quantum computer via a variational approach, Nat. Commun. 12, 6499 (2021).
  43. I. Raychowdhury and J. R. Stryker, Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories, Phys. Rev. D 101, 114502 (2020).
  44. 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).
  45. 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).
  46. 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).
  47. T. Byrnes and Y. Yamamoto, Simulating lattice gauge theories on a quantum computer, Phys. Rev. A 73, 022328 (2006).
  48. Z. Davoudi, , TASI/CERN/KITP Lecture notes on toward quantum computing gauge theories of Nature, arXiv:2507.15840.
  49. 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).
  50. J. B. Kogut and L. Susskind, Hamiltonian formulation of Wilson’s lattice gauge theories, Phys. Rev. D 11, 395 (1975).
  51. J. B. Kogut, An introduction to lattice gauge theory and spin systems, Rev. Mod. Phys. 51, 659 (1979).
  52. L. D. McLerran and R. Venugopalan, Gluon distribution functions for very large nuclei at small transverse momentum, Phys. Rev. D 49, 3352 (1994).
  53. L. D. McLerran and R. Venugopalan, Computing quark and gluon distribution functions for very large nuclei, Phys. Rev. D 49, 2233 (1994).
  54. L. D. McLerran and R. Venugopalan, Green’s functions in the color field of a large nucleus, Phys. Rev. D 50, 2225 (1994).
  55. Y. V. Kovchegov and E. Levin, Quantum Chromodynamics at High Energy, Vol. 33 (Oxford University Press, New York, 2013).
  56. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols (World Scientific, Singapore, 1988).
  57. R. Sagastizabal, S. P. Premaratne, B. A. Klaver, A. Rol, N. Haider, A. Bruno, A. Y. Matsuura, and L. DiCarlo, Variational preparation of finite-temperature states on a quantum computer, npj Quantum Inf. 7, 130 (2021).
  58. Z. Hu, R. Xia, and S. Kais, A quantum algorithm for evolving open quantum dynamics on quantum computing devices, Sci. Rep. 10, 3301 (2020).
  59. Z. Ding, X. Li, and L. Lin, Simulating open quantum systems using Hamiltonian simulations, PRX Quantum 5, 020332 (2024).
  60. A. W. Schlimgen, K. Head-Marsden, L. M. Sager-Smith, P. Narang, and D. A. Mazziotti, Quantum simulation of open quantum systems using a unitary decomposition of operators, Phys. Rev. Lett. 127, 270503 (2021).
  61. A. W. Schlimgen, K. Head-Marsden, L. M. Sager-Smith, P. Narang, and D. A. Mazziotti, Quantum simulation of the Lindblad equation using a unitary decomposition of operators, Phys. Rev. Res. 4, 023216 (2022).
  62. A. W. Schlimgen, K. Head-Marsden, L. M. Sager-Smith, P. Narang, and D. A. Mazziotti, Quantum simulation of open quantum systems using density-matrix purification, arXiv:2207.07112.
  63. A. Gaikwad, Arvind, and K. Dorai, Simulating open quantum dynamics on an NMR quantum processor using the Sz.-Nagy dilation algorithm, Phys. Rev. A 106, 022424 (2022).
  64. R. Cleve and C. Wang, Efficient quantum algorithms for simulating Lindblad evolution, in Proceedings of the 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017), LIPIcs, Vol. 80 (2017), pp. 17:1–17:14.
  65. E. Borras and M. Marvian, Quantum algorithms based on quantum trajectories, arXiv:2509.10425.
  66. Z. Ding, X. Li, and L. Lin, Simulating open quantum systems using Hamiltonian simulations, PRX Quantum 5, 020332 (2024).
  67. G. Di Bartolomeo, M. Vischi, T. Feri, A. Bassi, and S. Donadi, Efficient quantum algorithm to simulate open systems through a single environmental qubit, Phys. Rev. Res. 6, 043321 (2024).
  68. H. Kamakari, S.-N. Sun, M. Motta, and A. J. Minnich, Digital quantum simulation of open quantum systems using quantum imaginary–time evolution, PRX Quantum 3, 010320 (2022).
  69. T. Watad and N. H. Lindner, Variational quantum algorithms for simulation of Lindblad dynamics, Quantum Sci. Technol. 9, 025015 (2024).
  70. H. Chen, N. Gomes, S. Niu, and Wibe Albert de Jong, Adaptive variational simulation for open quantum systems, Quantum 8, 1252 (2024).
  71. L. Gravina and V. Savona, Adaptive variational low-rank dynamics for open quantum systems, Phys. Rev. Res. 6, 023072 (2024).
  72. L. E. Ratcliff et al., Quantum algorithms and applications for open quantum systems, Chem. Rev. 125, 1823 (2025).
  73. A. M. Childs and Y. Su, Nearly optimal lattice simulation by product formulas, Phys. Rev. Lett. 111, 060501 (2013).
  74. L. F. Richardson and J. A. Gaunt, The deferred approach to the limit, Phil. Trans. R. Soc. A 226, 299 (1927).
  75. M. Möttönen and J. J. Vartiainen, Decompositions of general quantum gates, Trends in Quantum Computing Research (NOVA Publishers, New York, 2005).
  76. E. T. Campbell, Random compiler for fast Hamiltonian simulation, Phys. Rev. Lett. 123, 200502 (2019).
  77. V. Bergholm, J. J. Vartiainen, M. Möttönen, and M. M. Salomaa, Quantum circuits with uniformly controlled one-qubit gates, Phys. Rev. A 71, 052330 (2005).
  78. A. A. Zecchi, C. Sanavio, S. Perotto, and S. Succi, Improved amplitude amplification strategies for the quantum simulation of classical transport problems, Quantum Sci. Technol. 10, 035039 (2025).
  79. A. Javadi-Abhari, M. Treinish, K. Krsulich, C. J. Wood, J. Lishman, J. Gacon, S. Martiel, P. D. Nation, L. S. Bishop, A. W. Cross, B. R. Johnson, and J. M. Gambetta, Quantum computing with qiskit, arXiv:2405.08810.
  80. M. Vu, Y. Li, K. Mueller et al., Hybrid continuous-discrete-variable quantum computing, arXiv:2511.13882.
  81. K. G. Fedorov, E. O. Kiktenko, M. A. Man’ko, V. I. Man’ko, and S. N. Filippov, Negativity volume of the generalized Wigner function as an entanglement witness for hybrid bipartite states, Sci. Rep. 8, 16240 (2018).
  82. C. Mauron and T. C. Ralph, Comparison of techniques for distillation of entanglement over a lossy channel, Phys. Rev. A 106, 062603 (2022).

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Phys. Rev. D 113, 114047– Published 25 June, 2026
  • Received 23 March 2026
  • Accepted 3 June 2026
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