• [1]

    F. Sauter, Z. Phys. 69, 742 (1931)

  • [2]

    W. Heisenberg and H. Euler, Z. Phys. 98, 714 (1936)

  • [3]

    J. Schwinger, Phys. Rev. 82, 664 (1951)

  • [4]

    E. Brezin and C. Itzykson, Phys. Rev. D 2, 1191 (1970)

  • [5]

    V. S. Popov, Sov. Phys. JETP 34, 709 (1972)

  • [6]

    A. Ringwald, Phys. Lett. B 510, 107 (2001)

  • [7]

    R. Alkofer, M. B. Hecht, C. D. Roberts, et al., Phys. Rev. Lett. 87, 193902 (2001)

  • [8]

    G. V. Dunne, Eur. Phys. J. D 55, 327 (2009)

  • [9]

    B. Buyens, J. Haegeman, F. Hebenstreit, et al., Phys. Rev. D 96, 114501 (2017)

  • [10]

    T. V. Zache, N. Mueller, J. T. Schneider, et al., Phys. Rev. Lett. 122, 050403 (2019)

  • [11]

    A. F. Shaw, P. Lougovski, J. R. Stryker, et al., Quantum 4, 306 (2020)

  • [12]

    L. Nagano, A. Bapat, and C. W. Bauer, Phys. Rev. D 108, 034501 (2023)

  • [13]

    K. G. Wilson, Phys. Rev. D 10, 2445 (1974)

  • [14]

    J. Kogut and L. Susskind, Phys. Rev. D 11, 395 (1975)

  • [15]

    J. B. Kogut, Rev. Mod. Phys. 51, 659 (1979)

  • [16]

    M. Creutz, Quarks, Gluons and Lattices (Cambridge: Cambridge University Press, 1983)

  • [17]

    I. Montvay and G. Münster, Quantum Fields on a Lattice (Cambridge: Cambridge University Press, 1994)

  • [18]

    M. Troyer and U.-J. Wiese, Phys. Rev. Lett. 94, 170201 (2005)

  • [19]

    P. de Forcrand, Simulating QCD at finite density, PoS LAT2009, 010 (2009)

  • [20]

    G. Aarts, Complex Langevin dynamics and other approaches at finite chemical potential, PoS LATTICE2012, 017 (2012)

  • [21]

    R. P. Feynman, Int. J. Theor. Phys. 21, 467 (1982)

  • [22]

    S. Lloyd, Science 273, 1073 (1996)

  • [23]

    S. P. Jordan, K. S. M. Lee, and J. Preskill, Science 336, 1130 (2012)

  • [24]

    J. Preskill, Quantum 2, 79 (2018)

  • [25]

    J. Schwinger, Phys. Rev. 128, 2425 (1962)

  • [26]

    J. H. Lowenstein and J. A. Swieca, Ann. Phys. (N.Y.) 68, 172 (1971)

  • [27]

    S. Coleman, R. Jackiw, and L. Susskind, Ann. Phys. (N.Y.) 93, 267 (1975)

  • [28]

    S. Coleman, Ann. Phys. (N.Y.) 101, 239 (1976)

  • [29]

    A. Casher, J. Kogut, and L. Susskind, Phys. Rev. D 10, 732 (1974)

  • [30]

    T. Banks, L. Susskind, and J. Kogut, Phys. Rev. D 13, 1043 (1976)

  • [31]

    C. J. Hamer, Z. Weihong, and J. Oitmaa, Phys. Rev. D 56, 55 (1997)

  • [32]

    T. Byrnes, P. Sriganesh, R. J. Bursill, et al., Phys. Rev. D 66, 013002 (2002)

  • [33]

    M. C. Bañuls, K. Cichy, J. I. Cirac, et al., JHEP 11, 158 (2013)

  • [34]

    B. Buyens, J. Haegeman, K. Van Acoleyen, et al., Phys. Rev. Lett. 113, 091601 (2014)

  • [35]

    B. Buyens, F. Verstraete, and K. Van Acoleyen, Phys. Rev. D 94, 085018 (2016)

  • [36]

    L. Funcke, K. Jansen, and S. Kühn, Phys. Rev. D 101, 054507 (2020)

  • [37]

    P. Jordan and E. Wigner, Z. Phys. 47, 631 (1928)

  • [38]

    M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge: Cambridge University Press, 2000)

  • [39]

    G. Ortiz, J. E. Gubernatis, E. Knill, et al., Phys. Rev. A 64, 022319 (2001)

  • [40]

    I. M. Georgescu, S. Ashhab, and F. Nori, Rev. Mod. Phys. 86, 153 (2014)

  • [41]

    U.-J. Wiese, Ann. Phys. (Berlin) 525, 777 (2013)

  • [42]

    E. Zohar, J. I. Cirac, and B. Reznik, Rep. Prog. Phys. 79, 014401 (2016)

  • [43]

    M. C. Bañuls, R. Blatt, J. Catani, et al., Eur. Phys. J. D 74, 165 (2020)

  • [44]

    C. W. Bauer, Z. Davoudi, A. B. Balantekin, et al., PRX Quantum 4, 027001 (2023)

  • [45]

    D. Banerjee, M. Dalmonte, M. Müller, et al., Phys. Rev. Lett. 109, 175302 (2012)

  • [46]

    E. Zohar, J. I. Cirac, and B. Reznik, Phys. Rev. Lett. 109, 125302 (2012)

  • [47]

    D. Banerjee, M. Bögli, M. Dalmonte, et al., Phys. Rev. Lett. 110, 125303 (2013)

  • [48]

    E. Zohar, A. Farace, B. Reznik, et al., Phys. Rev. A 95, 023604 (2017)

  • [49]

    E. A. Martinez, C. A. Muschik, P. Schindler, et al., Nature 534, 516 (2016)

  • [50]

    N. Klco, E. F. Dumitrescu, A. J. McCaskey, et al., Phys. Rev. A 98, 032331 (2018)

  • [51]

    C. Kokail, C. Maier, R. van Bijnen, et al., Nature 569, 355 (2019)

  • [52]

    F. M. Surace, P. P. Mazza, G. Giudici, et al., Phys. Rev. X 10, 021041 (2020)

  • [53]

    J. R. Stryker, Phys. Rev. A 99, 042301 (2019)

  • [54]

    N. H. Nguyen, M. C. Tran, Y. Zhu, et al., PRX Quantum 3, 020324 (2022)

  • [55]

    W. A. de Jong, K. Lee, J. Mulligan, et al., Phys. Rev. D 106, 054508 (2022)

  • [56]

    X.-D. Xie, X. Guo, H. Xing, et al., Phys. Rev. D 106, 054509 (2022)

  • [57]

    M. Honda, E. Itou, Y. Kikuchi, et al., Phys. Rev. D 105, 014504 (2022)

  • [58]

    B. Chakraborty, M. Honda, T. Izubuchi, et al., Phys. Rev. D 105, 094503 (2022)

  • [59]

    T. Angelides, P. Naredi, A. Crippa, et al., npj Quantum Inf. 11, 6 (2025)

  • [60]

    O. Kaikov, T. Saporiti, V. Sazonov, et al., Phys. Rev. A 111, 062202 (2025)

  • [61]

    G. Zhang, X. Guo, E. Wang, et al., Phys. Rev. D 111, 056031 (2025)

  • [62]

    B. Yang, H. Sun, R. Ott, et al., Nature 587, 392 (2020)

  • [63]

    Z.-Y. Zhou, G.-X. Su, J. C. Halimeh, et al., Science 377, 311 (2022)

  • [64]

    G.-X. Su, H. Sun, A. Hudomal, et al., Phys. Rev. Res. 5, 023010 (2023)

  • [65]

    J. C. Halimeh, I. P. McCulloch, B. Yang, et al., PRX Quantum 3, 040316 (2022)

  • [66]

    W.-Y. Zhang, Y. Liu, Y. Cheng, et al., Nat. Phys. 21, 155 (2025)

  • [67]

    G.-X. Su, J. J. Osborne, and J. C. Halimeh, PRX Quantum 5, 040310 (2024)

  • [68]

    J. Schuhmacher, G.-X. Su, J. J. Osborne, et al., arXiv: 2505.20387

  • [69]

    R. Joshi, Y. Tian, K. Hemery, et al., arXiv: 2604.07436

  • [70]

    A. Di Meglio, K. Jansen, I. Tavernelli, et al., PRX Quantum 5, 037001 (2024)

  • [71]

    J. C. Halimeh, N. Mueller, J. Knolle, et al., arXiv: 2509.03586

  • [72]

    S. Gupta and L. Santos, Phys. Rev. A 114, 033321 (2026)

  • [73]

    A. Peruzzo, J. McClean, P. Shadbolt, et al., Nat. Commun. 5, 4213 (2014)

  • [74]

    J. R. McClean, J. Romero, R. Babbush, et al., New J. Phys. 18, 023023 (2016)

  • [75]

    A. Kandala, A. Mezzacapo, K. Temme, et al., Nature 549, 242 (2017)

  • [76]

    M. Cerezo, A. Arrasmith, R. Babbush, et al., Nat. Rev. Phys. 3, 625 (2021)

  • [77]

    H. F. Trotter, Proc. Am. Math. Soc. 10, 545 (1959)

  • [78]

    M. Suzuki, Commun. Math. Phys. 51, 183 (1976)

  • [79]

    M. Suzuki, Phys. Lett. A 146, 319 (1990)

  • [80]

    D. W. Berry, A. M. Childs, R. Cleve, et al., Phys. Rev. Lett. 114, 090502 (2015)

  • [81]

    A. M. Childs, Y. Su, M. C. Tran, et al., Phys. Rev. X 11, 011020 (2021)

  • [82]

    A. Javadi-Abhari, M. Treinish, K. Krsulich, et al., arXiv: 2405.08810

  • [83]

    G. Aleksandrowicz, T. Alexander, P. Barkoutsos, et al., Qiskit: An Open-source Framework for Quantum Computing, Zenodo (2019), doi: 10.5281/zenodo.2562111

  • [84]

    J. R. McClean, S. Boixo, V. N. Smelyanskiy, et al., Nat. Commun. 9, 4812 (2018)

  • [85]

    O. Higgott, D. Wang, and S. Brierley, Quantum 3, 156 (2019)

  • [86]

    P. Virtanen, R. Gommers, T. E. Oliphant, et al., Nat. Methods 17, 261 (2020)

  • [87]

    C. R. Harris, K. J. Millman, S. J. van der Walt, et al., Nature 585, 357 (2020)

  • [88]

    J. D. Hunter, Comput. Sci. Eng. 9, 90 (2007)