Quantum Algorithms for Simulating the Lattice Schwinger Model

Alexander F. Shaw1,5, Pavel Lougovski1, Jesse R. Stryker2, and Nathan Wiebe3,4

1Quantum Information Science Group, Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, U.S.A.
2Institute for Nuclear Theory, University of Washington, Seattle, WA 98195-1550, U.S.A.
3Department of Physics, University of Washington, Seattle, WA 98195, U.S.A.
4Pacific Northwest National Laboratory, Richland, WA 99354, U.S.A.
5Department of Physics, University of Maryland, College Park, Maryland 20742, U.S.A.

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The Schwinger model (quantum electrodynamics in 1+1 dimensions) is a testbed for the study of quantum gauge field theories. We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In particular, we perform a tight analysis of low-order Trotter formula simulations of the Schwinger model, using recently derived commutator bounds, and give upper bounds on the resources needed for simulations in both scenarios. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x^{-1/2}$ and electric field cutoff $x^{-1/2}\Lambda$ can be simulated on a quantum computer for time $2xT$ using a number of $T$-gates or CNOTs in $\widetilde{O}( N^{3/2} T^{3/2} \sqrt{x} \Lambda )$ for fixed operator error. This scaling with the truncation $\Lambda$ is better than that expected from algorithms such as qubitization or QDRIFT. Furthermore, we give scalable measurement schemes and algorithms to estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable–the mean pair density. Finally, we bound the root-mean-square error in estimating this observable via simulation as a function of the diamond distance between the ideal and actual CNOT channels. This work provides a rigorous analysis of simulating the Schwinger model, while also providing benchmarks against which subsequent simulation algorithms can be tested.

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[1] D Aharonov. Quantum circuits with mixed states. In Proc. 30th Annual ACM Symposium on Theory of Computing, 1998. ACM Press, 1998. 10.1145/​276698.276708.

[2] Dorit Aharonov, Amnon Ta-Shma, and Amnon Ta-Shma. Adiabatic quantum state generation and statistical zero knowledge. In Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, pages 20–29. ACM, 2003. 10.1145/​780542.780546.

[3] Andrei Alexandru, Paulo F. Bedaque, Siddhartha Harmalkar, Henry Lamm, Scott Lawrence, and Neill C. Warrington. Gluon field digitization for quantum computers. Phys. Rev. D, 100: 114501, Dec 2019. 10.1103/​PhysRevD.100.114501.

[4] A. Avkhadiev, P. E. Shanahan, and R. D. Young. Accelerating lattice quantum field theory calculations via interpolator optimization using noisy intermediate-scale quantum computing. Phys. Rev. Lett., 124: 080501, Feb 2020. 10.1103/​PhysRevLett.124.080501.

[5] Ryan Babbush, Jarrod McClean, Dave Wecker, Alán Aspuru-Guzik, and Nathan Wiebe. Chemical basis of Trotter-Suzuki errors in quantum chemistry simulation. Physical Review A, 91 (2): 022311, 2015. 10.1103/​PhysRevA.91.022311.

[6] D. Banerjee, M. Bögli, M. Dalmonte, E. Rico, P. Stebler, Uwe-Jens Wiese, and P. Zoller. Atomic Quantum Simulation of ${{\mathrm{U}(N)}}$ and ${{\mathrm{SU}(N)}}$ Non-Abelian Lattice Gauge Theories. Phys. Rev. Lett., 110 (12): 125303, Mar 2013. 10.1103/​PhysRevLett.110.125303.

[7] T. Banks, Leonard Susskind, and John Kogut. Strong-coupling calculations of lattice gauge theories: (1 + 1)-dimensional exercises. Physical Review D, 13 (4): 1043–1053, Feb 1976. 10.1103/​PhysRevD.13.1043.

[8] Mari Carmen Bañuls, Rainer Blatt, Jacopo Catani, Alessio Celi, Juan Ignacio Cirac, Marcello Dalmonte, Leonardo Fallani, Karl Jansen, Maciej Lewenstein, Simone Montangero, Christine A. Muschik, Benni Reznik, Enrique Rico, Luca Tagliacozzo, Karel Van Acoleyen, Frank Verstraete, Uwe-Jens Wiese, Matthew Wingate, Jakub Zakrzewski, and Peter Zoller. Simulating lattice gauge theories within quantum technologies. The European Physical Journal D, 74 (8): 165, Aug 2020. ISSN 1434-6079. 10.1140/​epjd/​e2020-100571-8.

[9] Adriano Barenco, Charles H Bennett, Richard Cleve, David P DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A Smolin, and Harald Weinfurter. Elementary gates for quantum computation. Physical review A, 52 (5): 3457, 1995. 10.1103/​PhysRevA.52.3457.

[10] S. R. Beane, E. Chang, S. D. Cohen, W. Detmold, H. W. Lin, T. C. Luu, K. Orginos, A. Parreno, M. J. Savage, and A. Walker-Loud. Hyperon-Nucleon Interactions and the Composition of Dense Nuclear Matter from Quantum Chromodynamics. Phys. Rev. Lett., 109: 172001, 2012. 10.1103/​PhysRevLett.109.172001.

[11] S. R. Beane, E. Chang, S. D. Cohen, William Detmold, H. W. Lin, T. C. Luu, K. Orginos, A. Parreno, M. J. Savage, and A. Walker-Loud. Light Nuclei and Hypernuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry. Phys. Rev. D, 87 (3): 034506, 2013. 10.1103/​PhysRevD.87.034506.

[12] Dominic W Berry, Graeme Ahokas, Richard Cleve, and Barry C Sanders. Efficient quantum algorithms for simulating sparse Hamiltonians. Communications in Mathematical Physics, 270 (2): 359–371, 2007. 10.1007/​s00220-006-0150-x.

[13] Dominic W Berry, Andrew M Childs, Richard Cleve, Robin Kothari, and Rolando D Somma. Simulating hamiltonian dynamics with a truncated taylor series. Physical Review Letters, 114 (9): 090502, 2015. 10.1103/​PhysRevLett.114.090502.

[14] Dominic W. Berry, Andrew M. Childs, Yuan Su, Xin Wang, and Nathan Wiebe. Time-dependent Hamiltonian simulation with $L^1$-norm scaling. Quantum, 4: 254, Apr 2020. ISSN 2521-327X. 10.22331/​q-2020-04-20-254.

[15] Alex Bocharov, Martin Roetteler, and Krysta M Svore. Efficient synthesis of universal repeat-until-success quantum circuits. Physical Review Letters, 114 (8): 080502, 2015. 10.1103/​PhysRevLett.114.080502.

[16] Bruce M Boghosian and Washington Taylor IV. Simulating quantum mechanics on a quantum computer. Physica D: Nonlinear Phenomena, 120 (1-2): 30–42, 1998. 10.1016/​S0167-2789(98)00042-6.

[17] Gilles Brassard, Peter Hoyer, Michele Mosca, and Alain Tapp. Quantum amplitude amplification and estimation. Contemporary Mathematics, 305: 53–74, 2002. 10.1090/​conm/​305/​05215.

[18] Sergey Bravyi and Jeongwan Haah. Magic-state distillation with low overhead. Physical Review A, 86 (5): 052329, 2012. 10.1103/​PhysRevA.86.052329.

[19] Tim Byrnes and Yoshihisa Yamamoto. Simulating Lattice Gauge Theories on a Quantum Computer. Phys. Rev. A, 73 (2): 022328, Feb 2006. 10.1103/​PhysRevA.73.022328.

[20] Earl Campbell. Random compiler for fast Hamiltonian simulation. Physical Review Letters, 123 (7): 070503, 2019. 10.1103/​PhysRevLett.123.070503.

[21] Andrew M Childs and Robin Kothari. Simulating sparse Hamiltonians with star decompositions. In Conference on Quantum Computation, Communication, and Cryptography, pages 94–103. Springer, 2010. 10.1007/​978-3-642-18073-6_8.

[22] Andrew M Childs and Nathan Wiebe. Hamiltonian simulation using linear combinations of unitary operations. Quantum Information & Computation, 12 (11-12): 901–924, 2012.

[23] Andrew M Childs, Dmitri Maslov, Yunseong Nam, Neil J Ross, and Yuan Su. Toward the first quantum simulation with quantum speedup. Proceedings of the National Academy of Sciences, 115 (38): 9456–9461, 2018. 10.1073/​pnas.1801723115.

[24] Andrew M. Childs, Yuan Su, Minh C. Tran, Nathan Wiebe, and Shuchen Zhu. A theory of trotter error. arXiv:1912.08854, 2019.

[25] L. Contessi, A. Lovato, F. Pederiva, A. Roggero, J. Kirscher, and U. van Kolck. Ground-state properties of $^{4}$He and $^{16}$O extrapolated from lattice QCD with pionless EFT. Phys. Lett. B, 772: 839–848, 2017. 10.1016/​j.physletb.2017.07.048.

[26] Michael Creutz. Monte Carlo study of quantized SU (2) gauge theory. Phys. Rev. D, 21 (8): 2308, 1980. 10.1103/​PhysRevD.21.2308.

[27] Zohreh Davoudi, Mohammad Hafezi, Christopher Monroe, Guido Pagano, Alireza Seif, and Andrew Shaw. Towards analog quantum simulations of lattice gauge theories with trapped ions. Phys. Rev. Research, 2: 023015, Apr 2020. 10.1103/​PhysRevResearch.2.023015.

[28] Thomas G. Draper, Samuel A. Kutin, Eric M. Rains, and Krysta M. Svore. A logarithmic-depth quantum carry-lookahead adder. Quantum Info. Comput., 6 (4): 351–369, Jul 2006. ISSN 1533-7146.

[29] Bryan Eastin and Emanuel Knill. Restrictions on transversal encoded quantum gate sets. Physical Review Letters, 102 (11): 110502, 2009. 10.1103/​PhysRevLett.102.110502.

[30] Richard P. Feynman. Simulating physics with computers. International Journal of Theoretical Physics, 21 (6): 467–488, June 1982. ISSN 1572-9575. 10.1007/​BF02650179.

[31] Craig Gidney. Halving the cost of quantum addition. Quantum, 2 (74): 10–22331, 2018. 10.22331/​q-2018-06-18-74.

[32] András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe. Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pages 193–204. ACM, 2019. 10.1145/​3313276.3316366.

[33] Jeongwan Haah, Matthew Hastings, Robin Kothari, and Guang Hao Low. Quantum algorithm for simulating real time evolution of lattice hamiltonians. In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS), pages 350–360. IEEE, 2018. 10.1109/​FOCS.2018.00041.

[34] Siddhartha Harmalkar, Henry Lamm, and Scott Lawrence. Quantum Simulation of Field Theories Without State Preparation. arXiv:2001.11490 [hep-lat, physics:quant-ph], Jan 2020.

[35] Jacky Huyghebaert and Hans De Raedt. Product formula methods for time-dependent Schrodinger problems. Journal of Physics A: Mathematical and General, 23 (24): 5777, 1990. 10.1088/​0305-4470/​23/​24/​019.

[36] Takashi Inoue, Sinya Aoki, Bruno Charron, Takumi Doi, Tetsuo Hatsuda, Yoichi Ikeda, Noriyoshi Ishii, Keiko Murano, Hidekatsu Nemura, and Kenji Sasaki. Medium-heavy nuclei from nucleon-nucleon interactions in lattice QCD. Phys. Rev. C, 91 (1): 011001, 2015. 10.1103/​PhysRevC.91.011001.

[37] Takumi Iritani, Sinya Aoki, Takumi Doi, Shinya Gongyo, Tetsuo Hatsuda, Yoichi Ikeda, Takashi Inoue, Noriyoshi Ishii, Hidekatsu Nemura, and Kenji Sasaki. Systematics of the HAL QCD potential at low energies in lattice QCD. Phys. Rev. D, 99: 014514, Jan 2019. 10.1103/​PhysRevD.99.014514.

[38] Cody Jones. Low-overhead constructions for the fault-tolerant Toffoli gate. Physical Review A, 87 (2): 022328, 2013. 10.1103/​PhysRevA.87.022328.

[39] Stephen P. Jordan, Keith S. M. Lee, and John Preskill. Quantum algorithms for quantum field theories. Science, 336 (6085): 1130–1133, Jun 2012. ISSN 0036-8075, 1095-9203. 10.1126/​science.1217069.

[40] Stephen P. Jordan, Keith S. M. Lee, and John Preskill. Quantum computation of scattering in scalar quantum field theories. Quantum Info. Comput., 14 (11-12): 1014–1080, Sep 2014. ISSN 1533-7146.

[41] Johannes Kirscher, Nir Barnea, Doron Gazit, Francesco Pederiva, and Ubirajara van Kolck. Spectra and Scattering of Light Lattice Nuclei from Effective Field Theory. Phys. Rev. C, 92 (5): 054002, 2015. 10.1103/​PhysRevC.92.054002.

[42] Ian D Kivlichan, Nathan Wiebe, Ryan Babbush, and Alán Aspuru-Guzik. Bounding the costs of quantum simulation of many-body physics in real space. Journal of Physics A: Mathematical and Theoretical, 50 (30): 305301, 2017. 10.1088/​1751-8121/​aa77b8.

[43] Ian D Kivlichan, Jarrod McClean, Nathan Wiebe, Craig Gidney, Alán Aspuru-Guzik, Garnet Kin-Lic Chan, and Ryan Babbush. Quantum simulation of electronic structure with linear depth and connectivity. Physical Review Letters, 120 (11): 110501, 2018. 10.1103/​PhysRevLett.120.110501.

[44] N. Klco, E. F. Dumitrescu, A. J. McCaskey, T. D. Morris, R. C. Pooser, M. Sanz, E. Solano, P. Lougovski, and M. J. Savage. Quantum-classical computation of Schwinger model dynamics using quantum computers. Phys. Rev., A98 (3): 032331, 2018. 10.1103/​PhysRevA.98.032331.

[45] Natalie Klco and Martin J. Savage. Digitization of scalar fields for quantum computing. Phys. Rev., A99 (5): 052335, 2019. 10.1103/​PhysRevA.99.052335.

[46] Natalie Klco, Martin J. Savage, and Jesse R. Stryker. SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers. Phys. Rev. D, 101: 074512, Apr 2020. 10.1103/​PhysRevD.101.074512.

[47] Martin Kliesch, Christian Gogolin, and Jens Eisert. Lieb-Robinson bounds and the simulation of time-evolution of local observables in lattice systems. In Many-Electron Approaches in Physics, Chemistry and Mathematics, pages 301–318. Springer, 2014. 10.1007/​978-3-319-06379-9_17.

[48] John Kogut and Leonard Susskind. Hamiltonian formulation of Wilson's lattice gauge theories. Phys. Rev. D, 11: 395–408, Jan 1975. 10.1103/​PhysRevD.11.395.

[49] Benjamin P Lanyon, James D Whitfield, Geoff G Gillett, Michael E Goggin, Marcelo P Almeida, Ivan Kassal, Jacob D Biamonte, Masoud Mohseni, Ben J Powell, Marco Barbieri, et al. Towards quantum chemistry on a quantum computer. Nature chemistry, 2 (2): 106, 2010. 10.1038/​nchem.483.

[50] Seth Lloyd. Universal quantum simulators. Science, pages 1073–1078, 1996. 10.1126/​science.273.5278.1073.

[51] Guang Hao Low and Isaac L Chuang. Hamiltonian simulation by qubitization. Quantum, 3: 163, 2019. 10.22331/​q-2019-07-12-163.

[52] Alexandru Macridin, Panagiotis Spentzouris, James Amundson, and Roni Harnik. Electron-Phonon Systems on a Universal Quantum Computer. Phys. Rev. Lett., 121 (11): 110504, 2018. 10.1103/​PhysRevLett.121.110504.

[53] G. Magnifico, D. Vodola, E. Ercolessi, S. P. Kumar, M. Müller, and A. Bermudez. ${{{\mathbb{Z}}_{N}}}$ gauge theories coupled to topological fermions: ${{{\mathrm{QED}}}}_{2}$ with a quantum mechanical ${\theta}$ angle. Phys. Rev. B, 100: 115152, Sep 2019. 10.1103/​PhysRevB.100.115152.

[54] Esteban A. Martinez, Christine A. Muschik, Philipp Schindler, Daniel Nigg, Alexander Erhard, Markus Heyl, Philipp Hauke, Marcello Dalmonte, Thomas Monz, Peter Zoller, and Rainer Blatt. Real-Time Dynamics of Lattice Gauge Theories with a Few-Qubit Quantum Computer. Nature, 534 (7608): 516–519, Jun 2016. ISSN 1476-4687. 10.1038/​nature18318.

[55] A. Mezzacapo, E. Rico, C. Sabín, I. L. Egusquiza, L. Lamata, and E. Solano. Non-Abelian SU(2) Lattice Gauge Theories in Superconducting Circuits. Phys. Rev. Lett., 115 (24): 240502, Dec 2015. 10.1103/​PhysRevLett.115.240502.

[56] Christine Muschik, Markus Heyl, Esteban Martinez, Thomas Monz, Philipp Schindler, Berit Vogell, Marcello Dalmonte, Philipp Hauke, Rainer Blatt, and Peter Zoller. U(1) Wilson lattice gauge theories in digital quantum simulators. New J. Phys., 19 (10): 103020, 2017. ISSN 1367-2630. 10.1088/​1367-2630/​aa89ab.

[57] Michael A Nielsen and Isaac Chuang. Quantum computation and quantum information. AAPT, 2002. 10.1119/​1.1463744.

[58] NPLQCD Collaboration, Silas R. Beane, Emmanuel Chang, William Detmold, Kostas Orginos, Assumpta Parreño, Martin J. Savage, and Brian C. Tiburzi. Ab Initio Calculation of the $\mathrm{np}\rightarrow\mathrm{d}\gamma$ Radiative Capture Process. Phys. Rev. Lett., 115 (13): 132001, Sep 2015. 10.1103/​PhysRevLett.115.132001.

[59] NPLQCD Collaboration, Martin J. Savage, Phiala E. Shanahan, Brian C. Tiburzi, Michael L. Wagman, Frank Winter, Silas R. Beane, Emmanuel Chang, Zohreh Davoudi, William Detmold, and Kostas Orginos. Proton-Proton Fusion and Tritium $\beta$ Decay from Lattice Quantum Chromodynamics. Phys. Rev. Lett., 119 (6): 062002, Aug 2017. 10.1103/​PhysRevLett.119.062002.

[60] NuQS Collaboration, Henry Lamm, Scott Lawrence, and Yukari Yamauchi. General methods for digital quantum simulation of gauge theories. Phys. Rev. D, 100 (3): 034518, Aug 2019. 10.1103/​PhysRevD.100.034518.

[61] Maris Ozols, Martin Roetteler, and Jérémie Roland. Quantum rejection sampling. ACM Transactions on Computation Theory (TOCT), 5 (3): 1–33, 2013. 10.1145/​2493252.2493256.

[62] Indrakshi Raychowdhury and Jesse R Stryker. Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories. Physical Review D, 101 (11): 114502, 2020. 10.1103/​PhysRevD.101.114502.

[63] Markus Reiher, Nathan Wiebe, Krysta M Svore, Dave Wecker, and Matthias Troyer. Elucidating reaction mechanisms on quantum computers. Proceedings of the National Academy of Sciences, 114 (29): 7555–7560, 2017. 10.1073/​pnas.1619152114.

[64] E. Rico, T. Pichler, M. Dalmonte, P. Zoller, and S. Montangero. Tensor Networks for Lattice Gauge Theories and Atomic Quantum Simulation. Phys. Rev. Lett., 112 (20): 201601, May 2014. 10.1103/​PhysRevLett.112.201601.

[65] Christian Schweizer, Fabian Grusdt, Moritz Berngruber, Luca Barbiero, Eugene Demler, Nathan Goldman, Immanuel Bloch, and Monika Aidelsburger. Floquet Approach to $\mathbb{Z}_2$ Lattice Gauge Theories with Ultracold Atoms in Optical Lattices. Nat. Phys., 15 (11): 1168–1173, Nov 2019. ISSN 1745-2481. 10.1038/​s41567-019-0649-7.

[66] Julian Schwinger. Gauge invariance and mass. ii. Phys. Rev., 128: 2425–2429, Dec 1962. 10.1103/​PhysRev.128.2425.

[67] Rolando D. Somma. Quantum simulations of one dimensional quantum systems. arXiv:1503.06319, 2015.

[68] Rolando D Somma. A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation. Journal of Mathematical Physics, 57 (6): 062202, 2016. 10.1063/​1.4952761.

[69] Masuo Suzuki. General theory of fractal path integrals with applications to many-body theories and statistical physics. Journal of Mathematical Physics, 32 (2): 400–407, 1991. 10.1063/​1.529425.

[70] Krysta M. Svore, Matthew B. Hastings, and Michael Freedman. Faster phase estimation. Quantum Info. Comput., 14 (3-4): 306–328, March 2014. ISSN 1533-7146.

[71] L. Tagliacozzo, A. Celi, P. Orland, M. W. Mitchell, and M. Lewenstein. Simulation of non-Abelian gauge theories with optical lattices. Nat. Commun., 4: 2615, Oct 2013. ISSN 2041-1723. 10.1038/​ncomms3615.

[72] John Watrous. The theory of quantum information. Cambridge University Press, 2018. 10.1017/​9781316848142.

[73] Dave Wecker, Bela Bauer, Bryan K Clark, Matthew B Hastings, and Matthias Troyer. Gate-count estimates for performing quantum chemistry on small quantum computers. Physical Review A, 90 (2): 022305, 2014. 10.1103/​PhysRevA.90.022305.

[74] Dave Wecker, Matthew B Hastings, Nathan Wiebe, Bryan K Clark, Chetan Nayak, and Matthias Troyer. Solving strongly correlated electron models on a quantum computer. Physical Review A, 92 (6): 062318, 2015. 10.1103/​PhysRevA.92.062318.

[75] Nathan Wiebe and Chris Granade. Efficient bayesian phase estimation. Physical review letters, 117 (1): 010503, 2016. 10.1103/​PhysRevLett.117.010503.

[76] Nathan Wiebe and Martin Roetteler. Quantum arithmetic and numerical analysis using repeat-until-success circuits. Quantum Information & Computation, 16 (1-2): 134–178, 2016.

[77] Nathan Wiebe, Dominic Berry, Peter Høyer, and Barry C Sanders. Higher order decompositions of ordered operator exponentials. Journal of Physics A: Mathematical and Theoretical, 43 (6): 065203, 2010. 10.1088/​1751-8113/​43/​6/​065203.

[78] U.-J. Wiese. Ultracold quantum gases and lattice systems: Quantum simulation of lattice gauge theories. Ann. Phys., 525 (10-11): 777–796, 2013. ISSN 1521-3889. 10.1002/​andp.201300104.

[79] Uwe-Jens Wiese. Towards quantum simulating QCD. Nucl. Phys. A, 931: 246–256, Nov 2014. ISSN 0375-9474. 10.1016/​j.nuclphysa.2014.09.102.

[80] Kenneth G. Wilson. Confinement of quarks. Phys. Rev. D, 10: 2445–2459, Oct 1974. 10.1103/​PhysRevD.10.2445.

[81] T. Yamazaki, Y. Kuramashi, and A. Ukawa. Helium Nuclei in Quenched Lattice QCD. Phys. Rev. D, 81: 111504, 2010. 10.1103/​PhysRevD.81.111504.

[82] Takeshi Yamazaki, Ken-ichi Ishikawa, Yoshinobu Kuramashi, and Akira Ukawa. Helium nuclei, deuteron and dineutron in 2+1 flavor lattice QCD. Phys. Rev. D, 86: 074514, 2012. 10.1103/​PhysRevD.86.074514.

[83] Takeshi Yamazaki, Ken-ichi Ishikawa, Yoshinobu Kuramashi, and Akira Ukawa. Study of quark mass dependence of binding energy for light nuclei in 2+1 flavor lattice QCD. Phys. Rev. D, 92 (1): 014501, 2015. 10.1103/​PhysRevD.92.014501.

[84] Theodore J Yoder, Guang Hao Low, and Isaac L Chuang. Fixed-point quantum search with an optimal number of queries. Physical review letters, 113 (21): 210501, 2014. 10.1103/​PhysRevLett.113.210501.

[85] Christof Zalka. Simulating quantum systems on a quantum computer. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454 (1969): 313–322, 1998. 10.1098/​rspa.1998.0162.

[86] Erez Zohar, J. Ignacio Cirac, and Benni Reznik. Cold-Atom Quantum Simulator for SU(2) Yang-Mills Lattice Gauge Theory. Phys. Rev. Lett., 110 (12): 125304, Mar 2013. 10.1103/​PhysRevLett.110.125304.

[87] Erez Zohar, Alessandro Farace, Benni Reznik, and J. Ignacio Cirac. Digital Quantum Simulation of $\mathbb{{Z}}_2$ Lattice Gauge Theories with Dynamical Fermionic Matter. Phys. Rev. Lett., 118 (7): 070501, Feb 2017. 10.1103/​PhysRevLett.118.070501.

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[9] Anthony N. Ciavarella and Ivan A. Chernyshev, "Preparation of the SU(3) lattice Yang-Mills vacuum with variational quantum methods", Physical Review D 105 7, 074504 (2022).

[10] Nhung H. Nguyen, Minh C. Tran, Yingyue Zhu, Alaina M. Green, C. Huerta Alderete, Zohreh Davoudi, and Norbert M. Linke, "Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions", PRX Quantum 3 2, 020324 (2022).

[11] Nhung H. Nguyen, Muyuan Li, Alaina M. Green, C. Huerta Alderete, Yingyue Zhu, Daiwei Zhu, Kenneth R. Brown, and Norbert M. Linke, "Demonstration of Shor Encoding on a Trapped-Ion Quantum Computer", Physical Review Applied 16 2, 024057 (2021).

[12] Zohreh Davoudi, Norbert M. Linke, and Guido Pagano, "Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach", Physical Review Research 3 4, 043072 (2021).

[13] Minh C. Tran, Yuan Su, Daniel Carney, and Jacob M. Taylor, "Faster Digital Quantum Simulation by Symmetry Protection", PRX Quantum 2 1, 010323 (2021).

[14] João Barata, Wenjie Gong, and Raju Venugopalan, "Realtime dynamics of hyperon spin correlations from string fragmentation in a deformed four-flavor Schwinger model", Physical Review D 109 11, 116003 (2024).

[15] Masazumi Honda, Etsuko Itou, Yuta Kikuchi, Lento Nagano, and Takuya Okuda, "Classically emulated digital quantum simulation for screening and confinement in the Schwinger model with a topological term", Physical Review D 105 1, 014504 (2022).

[16] Priyanka Mukhopadhyay, Torin F. Stetina, and Nathan Wiebe, "Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian", PRX Quantum 5 1, 010345 (2024).

[17] Junyu Liu, Zimu Li, Han Zheng, Xiao Yuan, and Jinzhao Sun, "Towards a variational Jordan–Lee–Preskill quantum algorithm", Machine Learning: Science and Technology 3 4, 045030 (2022).

[18] Niklas Mueller, Joseph A. Carolan, Andrew Connelly, Zohreh Davoudi, Eugene F. Dumitrescu, and Kübra Yeter-Aydeniz, "Quantum Computation of Dynamical Quantum Phase Transitions and Entanglement Tomography in a Lattice Gauge Theory", PRX Quantum 4 3, 030323 (2023).

[19] Abhishek Rajput, Alessandro Roggero, and Nathan Wiebe, "Quantum error correction with gauge symmetries", npj Quantum Information 9 1, 41 (2023).

[20] Reinier van der Meer, Zichang Huang, Malaquias Correa Anguita, Dongxue Qu, Peter Hooijschuur, Hongguang Liu, Muxin Han, Jelmer J. Renema, and Lior Cohen, "Experimental simulation of loop quantum gravity on a photonic chip", npj Quantum Information 9 1, 32 (2023).

[21] Domenico Pomarico, Leonardo Cosmai, Paolo Facchi, Cosmo Lupo, Saverio Pascazio, and Francesco V. Pepe, "Dynamical Quantum Phase Transitions of the Schwinger Model: Real-Time Dynamics on IBM Quantum", Entropy 25 4, 608 (2023).

[22] Zohreh Davoudi, Alexander F. Shaw, and Jesse R. Stryker, "General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory", Quantum 7, 1213 (2023).

[23] Anthony N. Ciavarella, Stephan Caspar, Marc Illa, and Martin J. Savage, "State Preparation in the Heisenberg Model through Adiabatic Spiraling", Quantum 7, 970 (2023).

[24] Yu-An Chen, Andrew M. Childs, Mohammad Hafezi, Zhang Jiang, Hwanmun Kim, and Yijia Xu, "Efficient product formulas for commutators and applications to quantum simulation", Physical Review Research 4 1, 013191 (2022).

[25] Kazuki Ikeda, Dmitri E. Kharzeev, and Shuzhe Shi, "Nonlinear chiral magnetic waves", Physical Review D 108 7, 074001 (2023).

[26] Yu Tong, Victor V. Albert, Jarrod R. McClean, John Preskill, and Yuan Su, "Provably accurate simulation of gauge theories and bosonic systems", Quantum 6, 816 (2022).

[27] Roland C. Farrell, Ivan A. Chernyshev, Sarah J. M. Powell, Nikita A. Zemlevskiy, Marc Illa, and Martin J. Savage, "Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. II. Single-baryon β -decay in real time", Physical Review D 107 5, 054513 (2023).

[28] Robert Maxton and Yannick Meurice, "Perturbative boundaries of quantum advantage: Real-time evolution for digitized λϕ4 lattice models", Physical Review D 107 7, 074508 (2023).

[29] Clement Charles, Erik J. Gustafson, Elizabeth Hardt, Florian Herren, Norman Hogan, Henry Lamm, Sara Starecheski, Ruth S. Van de Water, and Michael L. Wagman, "Simulating Z2 lattice gauge theory on a quantum computer", Physical Review E 109 1, 015307 (2024).

[30] Muhammad Asaduzzaman, Goksu Can Toga, Simon Catterall, Yannick Meurice, and Ryo Sakai, "Quantum simulation of the N -flavor Gross-Neveu model", Physical Review D 106 11, 114515 (2022).

[31] Stephan Caspar and Hersh Singh, "From Asymptotic Freedom to θ Vacua: Qubit Embeddings of the O(3) Nonlinear σ Model", Physical Review Letters 129 2, 022003 (2022).

[32] Oriel Kiss, Michele Grossi, and Alessandro Roggero, "Importance sampling for stochastic quantum simulations", Quantum 7, 977 (2023).

[33] Vasily Sazonov and Mohamed Tamaazousti, "Quantum error mitigation for parametric circuits", Physical Review A 105 4, 042408 (2022).

[34] Ashley Milsted, Junyu Liu, John Preskill, and Guifre Vidal, "Collisions of False-Vacuum Bubble Walls in a Quantum Spin Chain", PRX Quantum 3 2, 020316 (2022).

[35] Abhishek Rajput, Alessandro Roggero, and Nathan Wiebe, "Hybridized Methods for Quantum Simulation in the Interaction Picture", Quantum 6, 780 (2022).

[36] Christian W. Bauer, Zohreh Davoudi, Natalie Klco, and Martin J. Savage, "Quantum simulation of fundamental particles and forces", Nature Reviews Physics 5 7, 420 (2023).

[37] Raka Dasgupta and Indrakshi Raychowdhury, "Cold-atom quantum simulator for string and hadron dynamics in non-Abelian lattice gauge theory", Physical Review A 105 2, 023322 (2022).

[38] S. Hasibul Hassan Chowdhury, Talal Ahmed Chowdhury, Salah Nasri, Omar Ibna Nazim, and Shaikh Saad, "Quantum simulation of quantum mechanical system with spatial noncommutativity", International Journal of Quantum Information 21 06, 2350028 (2023).

[39] Gumaro Rendon, Jacob Watkins, and Nathan Wiebe, "Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation", Quantum 8, 1266 (2024).

[40] Anthony N. Ciavarella, "Quantum simulation of lattice QCD with improved Hamiltonians", Physical Review D 108 9, 094513 (2023).

[41] Anthony Ciavarella, "Algorithm for quantum computation of particle decays", Physical Review D 102 9, 094505 (2020).

[42] Anthony Ciavarella, Natalie Klco, and Martin J. Savage, "Trailhead for quantum simulation of SU(3) Yang-Mills lattice gauge theory in the local multiplet basis", Physical Review D 103 9, 094501 (2021).

[43] Erik J. Gustafson, "Prospects for simulating a qudit-based model of (1+1)D scalar QED", Physical Review D 103 11, 114505 (2021).

[44] Yuan Su, Hsin-Yuan Huang, and Earl T. Campbell, "Nearly tight Trotterization of interacting electrons", Quantum 5, 495 (2021).

[45] Daniel González-Cuadra, Torsten V. Zache, Jose Carrasco, Barbara Kraus, and Peter Zoller, "Hardware Efficient Quantum Simulation of Non-Abelian Gauge Theories with Qudits on Rydberg Platforms", Physical Review Letters 129 16, 160501 (2022).

[46] Torsten V. Zache, Maarten Van Damme, Jad C. Halimeh, Philipp Hauke, and Debasish Banerjee, "Toward the continuum limit of a (1+1)D quantum link Schwinger model", Physical Review D 106 9, L091502 (2022).

[47] Danny Paulson, Luca Dellantonio, Jan F. Haase, Alessio Celi, Angus Kan, Andrew Jena, Christian Kokail, Rick van Bijnen, Karl Jansen, Peter Zoller, and Christine A. Muschik, "Simulating 2D Effects in Lattice Gauge Theories on a Quantum Computer", PRX Quantum 2 3, 030334 (2021).

[48] Jacob Bringewatt and Zohreh Davoudi, "Parallelization techniques for quantum simulation of fermionic systems", Quantum 7, 975 (2023).

[49] Marcela Carena, Henry Lamm, Ying-Ying Li, and Wanqiang Liu, "Lattice renormalization of quantum simulations", Physical Review D 104 9, 094519 (2021).

[50] Roland C. Farrell, Ivan A. Chernyshev, Sarah J. M. Powell, Nikita A. Zemlevskiy, Marc Illa, and Martin J. Savage, "Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. I. Axial gauge", Physical Review D 107 5, 054512 (2023).

[51] Zohreh Davoudi, Indrakshi Raychowdhury, and Andrew Shaw, "Search for efficient formulations for Hamiltonian simulation of non-Abelian lattice gauge theories", Physical Review D 104 7, 074505 (2021).

[52] Wibe A. de Jong, Mekena Metcalf, James Mulligan, Mateusz Płoskoń, Felix Ringer, and Xiaojun Yao, "Quantum simulation of open quantum systems in heavy-ion collisions", Physical Review D 104 5, L051501 (2021).

[53] Guang Hao Low, Yuan Su, Yu Tong, and Minh C. Tran, "Complexity of Implementing Trotter Steps", PRX Quantum 4 2, 020323 (2023).

[54] João Barata, Niklas Mueller, Andrey Tarasov, and Raju Venugopalan, "Single-particle digitization strategy for quantum computation of a ϕ4 scalar field theory", Physical Review A 103 4, 042410 (2021).

[55] Angus Kan and Yunseong Nam, "Simulating lattice quantum electrodynamics on a quantum computer", Quantum Science and Technology 8 1, 015008 (2023).

[56] Wibe A. de Jong, Kyle Lee, James Mulligan, Mateusz Płoskoń, Felix Ringer, and Xiaojun Yao, "Quantum simulation of nonequilibrium dynamics and thermalization in the Schwinger model", Physical Review D 106 5, 054508 (2022).

[57] Shane Thompson and George Siopsis, "Quantum computation of phase transition in the massive Schwinger model", Quantum Science and Technology 7 3, 035001 (2022).

[58] Lento Nagano, Aniruddha Bapat, and Christian W. Bauer, "Quench dynamics of the Schwinger model via variational quantum algorithms", Physical Review D 108 3, 034501 (2023).

[59] P. Achenbach, D. Adhikari, A. Afanasev, F. Afzal, C.A. Aidala, A. Al-bataineh, D.K. Almaalol, M. Amaryan, D. Androić, W.R. Armstrong, M. Arratia, J. Arrington, A. Asaturyan, E.C. Aschenauer, H. Atac, H. Avakian, T. Averett, C. Ayerbe Gayoso, X. Bai, K.N. Barish, N. Barnea, G. Basar, M. Battaglieri, A.A. Baty, I. Bautista, A. Bazilevsky, C. Beattie, S.C. Behera, V. Bellini, R. Bellwied, J.F. Benesch, F. Benmokhtar, C.A. Bernardes, J.C. Bernauer, H. Bhatt, S. Bhatta, M. Boer, T.J. Boettcher, S.A. Bogacz, H.J. Bossi, J.D. Brandenburg, E.J. Brash, R.A. Briceño, W.J. Briscoe, S.J. Brodsky, D.A. Brown, V.D. Burkert, H. Caines, I.A. Cali, A. Camsonne, D.S. Carman, J. Caylor, D.S. Cerci, S. Cerci, M. Chamizo Llatas, S. Chatterjee, J.P. Chen, Y. Chen, Y.-C. Chen, Y.-T. Chien, P.-C. Chou, X. Chu, E. Chudakov, E. Cline, I.C. Cloët, P.L. Cole, M.E. Connors, M. Constantinou, W. Cosyn, S. Covrig Dusa, R. Cruz-Torres, U. D'Alesio, C. da Silva, Z. Davoudi, C.T. Dean, D.J. Dean, M. Demarteau, A. Deshpande, W. Detmold, A. Deur, B.R. Devkota, S. Dhital, M. Diefenthaler, S. Dobbs, M. Döring, X. Dong, R. Dotel, K.A. Dow, E.J. Downie, J.L. Drachenberg, A. Dumitru, J.C. Dunlop, R. Dupre, J.M. Durham, D. Dutta, R.G. Edwards, R.J. Ehlers, L. El Fassi, M. Elaasar, L. Elouadrhiri, M. Engelhardt, R. Ent, S. Esumi, O. Evdokimov, O. Eyser, C. Fanelli, R. Fatemi, I.P. Fernando, F.A. Flor, N. Fomin, A.D. Frawley, T. Frederico, R.J. Fries, C. Gal, B.R. Gamage, L. Gamberg, H. Gao, D. Gaskell, F. Geurts, Y. Ghandilyan, N. Ghimire, R. Gilman, C. Gleason, K. Gnanvo, R.W. Gothe, S.V. Greene, H.W. Grießhammer, S.K. Grossberndt, B. Grube, D.C. Hackett, T.J. Hague, H. Hakobyan, J.-O. Hansen, Y. Hatta, M. Hattawy, L.B. Havener, O. Hen, W. Henry, D.W. Higinbotham, T.J. Hobbs, A.M. Hodges, T. Holmstrom, B. Hong, T. Horn, C.R. Howell, H.Z. Huang, M. Huang, S. Huang, G.M. Huber, C.E. Hyde, E.L. Isupov, P.M. Jacobs, J. Jalilian-Marian, A. Jentsch, H. Jheng, C.-R. Ji, X. Ji, J. Jia, D.C. Jones, M.K. Jones, S. Joosten, N. Kalantarians, G. Kalicy, Z.B. Kang, J.M. Karthein, D. Keller, C. Keppel, V. Khachatryan, D.E. Kharzeev, H. Kim, M. Kim, Y. Kim, P.M. King, E. Kinney, S.R. Klein, H.S. Ko, V. Koch, M. Kohl, Y.V. Kovchegov, G.K. Krintiras, V. Kubarovsky, S.E. Kuhn, K.S. Kumar, T. Kutz, J.G. Lajoie, J. Lauret, I. Lavrukhin, D. Lawrence, J.H. Lee, K. Lee, S. Lee, Y.-J. Lee, S. Li, W. Li, Xiaqing Li, Xuan Li, J. Liao, H.-W. Lin, M.A. Lisa, K.-F. Liu, M.X. Liu, T. Liu, S. Liuti, N. Liyanage, W.J. Llope, C. Loizides, R. Longo, W. Lorenzon, S. Lunkenheimer, X. Luo, R. Ma, B. McKinnon, D.G. Meekins, Y. Mehtar-Tani, W. Melnitchouk, A. Metz, C.A. Meyer, Z.-E. Meziani, R. Michaels, J.K.L. Michel, R.G. Milner, H. Mkrtchyan, P. Mohanmurthy, B. Mohanty, V.I. Mokeev, D.H. Moon, I.A. Mooney, C. Morningstar, D.P. Morrison, B. Müller, S. Mukherjee, J. Mulligan, C. Munoz Camacho, J.A. Murillo Quijada, M.J. Murray, S.A. Nadeeshani, P. Nadel-Turonski, J.D. Nam, C.E. Nattrass, G. Nijs, J. Noronha, J. Noronha-Hostler, N. Novitzky, M. Nycz, F.I. Olness, J.D. Osborn, R. Pak, B. Pandey, M. Paolone, Z. Papandreou, J.-F. Paquet, S. Park, K.D. Paschke, B. Pasquini, E. Pasyuk, T. Patel, A. Patton, C. Paudel, C. Peng, J.C. Peng, H. Pereira Da Costa, D.V. Perepelitsa, M.J. Peters, P. Petreczky, R.D. Pisarski, D. Pitonyak, M.A. Ploskon, M. Posik, J. Poudel, R. Pradhan, A. Prokudin, C.A. Pruneau, A.J.R. Puckett, P. Pujahari, J. Putschke, J.R. Pybus, J.-W. Qiu, K. Rajagopal, C. Ratti, K.F. Read, R. Reed, D.G. Richards, C. Riedl, F. Ringer, T. Rinn, J. Rittenhouse West, J. Roche, A. Rodas, G. Roland, F. Romero-López, P. Rossi, T. Rostomyan, L. Ruan, O.M. Ruimi, N.R. Saha, N.R. Sahoo, T. Sakaguchi, F. Salazar, C.W. Salgado, G. Salmè, S. Salur, S.N. Santiesteban, M.M. Sargsian, M. Sarsour, N. Sato, T. Satogata, S. Sawada, T. Schäfer, B. Scheihing-Hitschfeld, B. Schenke, S.T. Schindler, A. Schmidt, R. Seidl, M.H. Shabestari, P.E. Shanahan, C. Shen, T.-A. Sheng, M.R. Shepherd, A.M. Sickles, M.D. Sievert, K.L. Smith, Y. Song, A. Sorensen, P.A. Souder, N. Sparveris, S. Srednyak, A.G. Stahl Leiton, A.M. Stasto, P. Steinberg, S. Stepanyan, M. Stephanov, J.R. Stevens, D.J. Stewart, I.W. Stewart, M. Stojanovic, I. Strakovsky, S. Strauch, M. Strickland, D. Sunar Cerci, M. Suresh, B. Surrow, S. Syritsyn, A.P. Szczepaniak, A.S. Tadepalli, A.H. Tang, J.D. Tapia Takaki, T.J. Tarnowsky, A.N. Tawfik, M.I. Taylor, C. Tennant, A. Thiel, D. Thomas, Y. Tian, A.R. Timmins, P. Tribedy, Z. Tu, S. Tuo, T. Ullrich, E. Umaka, D.W. Upton, J.P. Vary, J. Velkovska, R. Venugopalan, A. Vijayakumar, I. Vitev, W. Vogelsang, R. Vogt, A. Vossen, E. Voutier, V. Vovchenko, A. Walker-Loud, F. Wang, J. Wang, X. Wang, X.-N. Wang, L.B. Weinstein, T.J. Wenaus, S. Weyhmiller, S.W. Wissink, B. Wojtsekhowski, C.P. Wong, M.H. Wood, Y. Wunderlich, B. Wyslouch, B.W. Xiao, W. Xie, W. Xiong, N. Xu, Q.H. Xu, Z. Xu, D. Yaari, X. Yao, Z. Ye, Z.H. Ye, C. Yero, F. Yuan, W.A. Zajc, C. Zhang, J. Zhang, F. Zhao, Y. Zhao, Z.W. Zhao, X. Zheng, J. Zhou, and M. Zurek, "The present and future of QCD", Nuclear Physics A 1047, 122874 (2024).

[60] Arata Yamamoto, "Real-time simulation of (2+1)-dimensional lattice gauge theory on qubits", Progress of Theoretical and Experimental Physics 2021 1, 013B06 (2021).

[61] Natalie Klco, Alessandro Roggero, and Martin J Savage, "Standard model physics and the digital quantum revolution: thoughts about the interface", Reports on Progress in Physics 85 6, 064301 (2022).

[62] Kyle Lee, James Mulligan, Felix Ringer, and Xiaojun Yao, "Liouvillian dynamics of the open Schwinger model: String breaking and kinetic dissipation in a thermal medium", Physical Review D 108 9, 094518 (2023).

[63] Kazuki Ikeda, Dmitri E. Kharzeev, and Yuta Kikuchi, "Real-time dynamics of Chern-Simons fluctuations near a critical point", Physical Review D 103 7, L071502 (2021).

[64] Torin F. Stetina, Anthony Ciavarella, Xiaosong Li, and Nathan Wiebe, "Simulating Effective QED on Quantum Computers", Quantum 6, 622 (2022).

[65] Jiayu Shen, Di Luo, Chenxi Huang, Bryan K. Clark, Aida X. El-Khadra, Bryce Gadway, and Patrick Draper, "Simulating quantum mechanics with a θ -term and an ’t Hooft anomaly on a synthetic dimension", Physical Review D 105 7, 074505 (2022).

[66] Robert D. Pisarski, "Wilson loops in the Hamiltonian formalism", Physical Review D 105 11, L111501 (2022).

[67] M. Sohaib Alam, Stuart Hadfield, Henry Lamm, and Andy C. Y. Li, "Primitive quantum gates for dihedral gauge theories", Physical Review D 105 11, 114501 (2022).

[68] Andrei Alexandru, Paulo F. Bedaque, Ruairí Brett, and Henry Lamm, "Spectrum of digitized QCD: Glueballs in a S(1080) gauge theory", Physical Review D 105 11, 114508 (2022).

[69] Arata Yamamoto, "Quantum variational approach to lattice gauge theory at nonzero density", Physical Review D 104 1, 014506 (2021).

[70] João Barata, Xiaojian Du, Meijian Li, Wenyang Qian, and Carlos A. Salgado, "Medium induced jet broadening in a quantum computer", Physical Review D 106 7, 074013 (2022).

[71] Christian W. Bauer, Zohreh Davoudi, A. Baha Balantekin, Tanmoy Bhattacharya, Marcela Carena, Wibe A. de Jong, Patrick Draper, Aida El-Khadra, Nate Gemelke, Masanori Hanada, Dmitri Kharzeev, Henry Lamm, Ying-Ying Li, Junyu Liu, Mikhail Lukin, Yannick Meurice, Christopher Monroe, Benjamin Nachman, Guido Pagano, John Preskill, Enrico Rinaldi, Alessandro Roggero, David I. Santiago, Martin J. Savage, Irfan Siddiqi, George Siopsis, David Van Zanten, Nathan Wiebe, Yukari Yamauchi, Kübra Yeter-Aydeniz, and Silvia Zorzetti, "Quantum Simulation for High-Energy Physics", PRX Quantum 4 2, 027001 (2023).

[72] Yu Tong, Dong An, Nathan Wiebe, and Lin Lin, "Fast inversion, preconditioned quantum linear system solvers, fast Green's-function computation, and fast evaluation of matrix functions", Physical Review A 104 3, 032422 (2021).

[73] Jacob Bringewatt, Jonathan Kunjummen, and Niklas Mueller, "Randomized measurement protocols for lattice gauge theories", Quantum 8, 1300 (2024).

[74] Christopher David White, ChunJun Cao, and Brian Swingle, "Conformal field theories are magical", Physical Review B 103 7, 075145 (2021).

[75] Xiaojun Yao, "SU(2) gauge theory in 2+1 dimensions on a plaquette chain obeys the eigenstate thermalization hypothesis", Physical Review D 108 3, L031504 (2023).

[76] Valentina Amitrano, Alessandro Roggero, Piero Luchi, Francesco Turro, Luca Vespucci, and Francesco Pederiva, "Trapped-ion quantum simulation of collective neutrino oscillations", Physical Review D 107 2, 023007 (2023).

[77] Enrico C. Domanti, Paolo Castorina, Dario Zappalà, and Luigi Amico, "Aharonov-Bohm effect for confined matter in lattice gauge theories", Physical Review Research 6 1, 013268 (2024).

[78] Berndt Müller and Xiaojun Yao, "Simple Hamiltonian for quantum simulation of strongly coupled (2+1)D SU(2) lattice gauge theory on a honeycomb lattice", Physical Review D 108 9, 094505 (2023).

[79] Dan-Bo Zhang, Hongxi Xing, Hui Yan, Enke Wang, and Shi-Liang Zhu, "Selected topics of quantum computing for nuclear physics* ", Chinese Physics B 30 2, 020306 (2021).

[80] Yao Ji, Henry Lamm, and Shuchen Zhu, "Gluon digitization via character expansion for quantum computers", Physical Review D 107 11, 114503 (2023).

[81] Yanting Cheng, Shang Liu, Wei Zheng, Pengfei Zhang, and Hui Zhai, "Tunable Confinement-Deconfinement Transition in an Ultracold-Atom Quantum Simulator", PRX Quantum 3 4, 040317 (2022).

[82] Ron Belyansky, Seth Whitsitt, Niklas Mueller, Ali Fahimniya, Elizabeth R. Bennewitz, Zohreh Davoudi, and Alexey V. Gorshkov, "High-Energy Collision of Quarks and Mesons in the Schwinger Model: From Tensor Networks to Circuit QED", Physical Review Letters 132 9, 091903 (2024).

[83] Yasar Y. Atas, Jan F. Haase, Jinglei Zhang, Victor Wei, Sieglinde M.-L. Pfaendler, Randy Lewis, and Christine A. Muschik, "Simulating one-dimensional quantum chromodynamics on a quantum computer: Real-time evolutions of tetra- and pentaquarks", Physical Review Research 5 3, 033184 (2023).

[84] Natalie Klco, D. H. Beck, and Martin J. Savage, "Entanglement structures in quantum field theories: Negativity cores and bound entanglement in the vacuum", Physical Review A 107 1, 012415 (2023).

[85] Peter J. Ehlers, "Entanglement between valence and sea quarks in hadrons of 1+1 dimensional QCD", Annals of Physics 452, 169290 (2023).

[86] Luis Hidalgo and Patrick Draper, "Quantum simulations for strong-field QED", Physical Review D 109 7, 076004 (2024).

[87] Emil Mathew and Indrakshi Raychowdhury, "Protecting local and global symmetries in simulating (1+1)D non-Abelian gauge theories", Physical Review D 106 5, 054510 (2022).

[88] Shane Thompson and George Siopsis, "Quantum computation of phase transition in interacting scalar quantum field theory", Quantum Information Processing 22 11, 396 (2023).

[89] Muhammad Azeem Akbar, Arif Ali Khan, and Saima Rafi, "A systematic decision-making framework for tackling quantum software engineering challenges", Automated Software Engineering 30 2, 22 (2023).

[90] Irian D’Andrea, Christian W. Bauer, Dorota M. Grabowska, and Marat Freytsis, "New basis for Hamiltonian SU(2) simulations", Physical Review D 109 7, 074501 (2024).

[91] Marc Illa and Martin J. Savage, "Basic elements for simulations of standard-model physics with quantum annealers: Multigrid and clock states", Physical Review A 106 5, 052605 (2022).

[92] Indrakshi Raychowdhury, "Toward quantum simulating non-Abelian gauge theories", Indian Journal of Physics 95 8, 1681 (2021).

[93] Zohreh Davoudi, Niklas Mueller, and Connor Powers, "Towards Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States", Physical Review Letters 131 8, 081901 (2023).

[94] S. Pathak, A. E. Russo, S. K. Seritan, and A. D. Baczewski, "Quantifying T -gate-count improvements for ground-state-energy estimation with near-optimal state preparation", Physical Review A 107 4, L040601 (2023).

[95] Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, and Fernando G. S. L. Brandão, "Quantum algorithms: A survey of applications and end-to-end complexities", arXiv:2310.03011, (2023).

[96] Andrew M. Childs, Yuan Su, Minh C. Tran, Nathan Wiebe, and Shuchen Zhu, "A Theory of Trotter Error", arXiv:1912.08854, (2019).

[97] Indrakshi Raychowdhury and Jesse R. Stryker, "Solving Gauss's law on digital quantum computers with loop-string-hadron digitization", Physical Review Research 2 3, 033039 (2020).

[98] Guang Hao Low, Yuan Su, Yu Tong, and Minh C. Tran, "On the complexity of implementing Trotter steps", arXiv:2211.09133, (2022).

[99] Indrakshi Raychowdhury and Jesse R. Stryker, "Solving Gauss's Law on Digital Quantum Computers with Loop-String-Hadron Digitization", arXiv:1812.07554, (2018).

[100] Ashley Milsted, Junyu Liu, John Preskill, and Guifre Vidal, "Collisions of false-vacuum bubble walls in a quantum spin chain", arXiv:2012.07243, (2020).

[101] Henry Lamm, Ying-Ying Li, Jing Shu, Yi-Lin Wang, and Bin Xu, "Block Encodings of Discrete Subgroups on Quantum Computer", arXiv:2405.12890, (2024).

[102] Marcela Carena, Henry Lamm, Ying-Ying Li, and Wanqiang Liu, "Quantum error thresholds for gauge-redundant digitizations of lattice field theories", arXiv:2402.16780, (2024).

[103] Arata Yamamoto, "Real-time simulation of (2+1)-dimensional lattice gauge theory on qubits", arXiv:2008.11395, (2020).

[104] Raghav G. Jha, "Notes on Quantum Computation and Information", arXiv:2301.09679, (2023).

[105] Minh C. Tran, Yuan Su, Daniel Carney, and Jacob M. Taylor, "Faster Digital Quantum Simulation by Symmetry Protection", arXiv:2006.16248, (2020).

[106] Kazuki Ikeda, "Quantum-classical simulation of quantum field theory by quantum circuit learning", arXiv:2311.16297, (2023).

[107] Dan-Bo Zhang, Hongxi Xing, Hui Yan, Enke Wang, and Shi-Liang Zhu, "Selected topics of quantum computing for nuclear physics", arXiv:2011.01431, (2020).

[108] Kazuki Ikeda and Adam Lowe, "Robustness of quantum correlation in quantum energy teleportation", arXiv:2402.00479, (2024).

[109] Ronak Desai, Yuan Feng, Mohammad Hassan, Abhishek Kodumagulla, and Michael McGuigan, "Z3 gauge theory coupled to fermions and quantum computing", arXiv:2106.00549, (2021).

[110] Ying Chen, Yunheng Ma, and Shun Zhou, "Quantum Simulations of the Non-Unitary Time Evolution and Applications to Neutral-Kaon Oscillations", arXiv:2105.04765, (2021).

[111] Robert Maxton and Yannick Meurice, "Perturbative boundaries of quantum computing: real-time evolution for digitized lambda phi^4 lattice models", arXiv:2210.05493, (2022).

[112] Tianyin Li, "Quantum simulations of quantum electrodynamics in Coulomb gauge", arXiv:2406.01204, (2024).

[113] L. Spagnoli, A. Roggero, and N. Wiebe, "Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes", arXiv:2405.19293, (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2024-06-22 10:46:36) and SAO/NASA ADS (last updated successfully 2024-06-22 10:46:38). The list may be incomplete as not all publishers provide suitable and complete citation data.

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