A resource efficient approach for quantum and classical simulations of gauge theories in particle physics

Jan F. Haase1,2, Luca Dellantonio1,2, Alessio Celi3,4, Danny Paulson1,2, Angus Kan1,2, Karl Jansen5, and Christine A. Muschik1,2,6

1Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1
2Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1
3Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
4Center for Quantum Physics, Faculty of Mathematics, Computer Science and Physics, University of Innsbruck, Innsbruck A-6020, Austria
5NIC, DESY, Platanenallee 6, D-15738 Zeuthen, Germany
6Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada, N2L 2Y5

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

Gauge theories establish the standard model of particle physics, and lattice gauge theory (LGT) calculations employing Markov Chain Monte Carlo (MCMC) methods have been pivotal in our understanding of fundamental interactions. The present limitations of MCMC techniques may be overcome by Hamiltonian-based simulations on classical or quantum devices, which further provide the potential to address questions that lay beyond the capabilities of the current approaches. However, for continuous gauge groups, Hamiltonian-based formulations involve infinite-dimensional gauge degrees of freedom that can solely be handled by truncation. Current truncation schemes require dramatically increasing computational resources at small values of the bare couplings, where magnetic field effects become important. Such limitation precludes one from `taking the continuous limit' while working with finite resources. To overcome this limitation, we provide a resource-efficient protocol to simulate LGTs with continuous gauge groups in the Hamiltonian formulation. Our new method allows for calculations at arbitrary values of the bare coupling and lattice spacing. The approach consists of the combination of a Hilbert space truncation with a regularization of the gauge group, which permits an efficient description of the magnetically-dominated regime. We focus here on Abelian gauge theories and use $2+1$ dimensional quantum electrodynamics as a benchmark example to demonstrate this efficient framework to achieve the continuum limit in LGTs. This possibility is a key requirement to make quantitative predictions at the field theory level and offers the long-term perspective to utilise quantum simulations to compute physically meaningful quantities in regimes that are precluded to quantum Monte Carlo.

Gauge theories are at the basis of the standard model, which describes fundamental particle interactions and thus the universe surrounding us. Besides other things, these theories tell us why particles bind together in nuclei to eventually form atoms and how they interact with each other. To mention a famous example where gauge theories have played a key role is the discovery of the Higgs boson which is responsible for the mass of the fundamental particles.
While the standard model, which is built on gauge theories,has already pushed the boundary of our knowledge, many open questions remain since their simulation is notoriously difficult in certain parameter regimes which are, however, important to understand physical phenomena such as the matter antimatter asymmetry of CP violation. Standard methods encounter problems that cannot or are extremely hardly be solved by using classical computing approaches — though quantum algorithms and hence quantum computers qualify as excellent candidates to drive another wave of innovations in particle physics.

In this work, we show how the gauge fields of a lattice gauge theory can be efficiently simulated. Generally, an exact description of the system requires an infinite amount of degrees of freedom, which practically cannot be taken into account. Therefore, any numerical method needs to apply a cutoff to these degrees of freedom, which in turn reduces the accuracy of the simulation. We provide a novel protocol leading to a cutoff, that allows for an efficient implementation of the problem. Importantly, it is applicable in both, quantum algorithms as well as classical simulation techniques. Furthermore, we provide the tools to estimate the error of the simulation if compared to the exact result from the untruncated theory. Our protocol is flexible and can be optimized for the available resources, for example the number of qubits in a quantum computer or the available memory in a classical machine.

As an application, we consider quantum electrodynamics in two spatial and one temporal dimensions as a benchmarking example. For intermediate values of the coupling – the most difficult regime – we reduce the required number of quantum states by one order of magnitude.
Our method will play an important role in the simulation of lattice gauge theories, whether they are quantum or classical and hence opens a path towards simulations of underlying models of the standard model of high energy physics, providing the possibility to address so far unanswered fundamental questions.

► BibTeX data

► References

[1] W. N. Cottingham and D. A. Greenwood, An Introduction to the Standard Model of Particle Physics, 2nd ed. (Cambridge University Press, 2007).
https:/​/​doi.org/​10.1017/​CBO9780511791406

[2] G. Altarelli, Collider Physics within the Standard Model, 1st ed., Lecture Notes in Physics, Vol. 937 (Springer International Publishing, 2017).
https:/​/​doi.org/​10.1007/​978-3-319-51920-3

[3] M. E. Peskin and D. V. Schroeder, An introduction to quantum field theory (CRC press, 2018).

[4] G. Altarelli, Frascati Phys. Ser. 58, 102 (2014).
arXiv:1407.2122

[5] M. J. Veltman, Facts and Mysteries in Elementary Particle Physics (World Scientific, 2018).
https:/​/​doi.org/​10.1142/​10904

[6] T. DeGrand and C. E. Detar, Lattice methods for quantum chromodynamics (World Scientific, 2006).
https:/​/​doi.org/​10.1142/​6065

[7] H. J. Rothe, Lattice Gauge Theories (World Scientific, 1992).
https:/​/​doi.org/​10.1142/​8229

[8] C. Gattringer and C. B. Lang, Quantum chromodynamics on the lattice, Vol. 788 (Springer, Berlin, 2010).
https:/​/​doi.org/​10.1007/​978-3-642-01850-3

[9] K. G. Wilson, Phys. Rev. D 10, 2445 (1974).
https:/​/​doi.org/​10.1103/​PhysRevD.10.2445

[10] S. Durr et al., Science 322, 1224 (2008).
https:/​/​doi.org/​10.1126/​science.1163233

[11] M. Constantinou, PoS CD15, 009 (2016).
https:/​/​doi.org/​10.22323/​1.253.0009

[12] A. Prokudin, K. Cichy, and M. Constantinou, Advances in High Energy Physics 2019, 3036904 (2019).
https:/​/​doi.org/​10.1155/​2019/​3036904

[13] H. B. Meyer and H. Wittig, Prog. Part. Nucl. Phys. 104, 46 (2019).
https:/​/​doi.org/​10.1016/​j.ppnp.2018.09.001

[14] A. Juttner, PoS LATTICE 2015, 006 (2016).
https:/​/​doi.org/​10.22323/​1.251.0006

[15] M. Troyer and U.-J. Wiese, Phys. Rev. Lett. 94, 170201 (2005).
https:/​/​doi.org/​10.1103/​PhysRevLett.94.170201

[16] M. C. Bañuls and K. Cichy, Rept. Prog. Phys. 83, 024401 (2020).
https:/​/​doi.org/​10.1088/​1361-6633/​ab6311

[17] M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen, and S. Kühn, Phys. Rev. Lett. 118, 071601 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.118.071601

[18] T. Sugihara, J. High Energy Phys. 2005, 022 (2005).
https:/​/​doi.org/​10.1088/​1126-6708/​2005/​07/​022

[19] L. Tagliacozzo, A. Celi, and M. Lewenstein, Phys. Rev. X 4, 041024 (2014).

[20] E. Rico, T. Pichler, M. Dalmonte, P. Zoller, and S. Montangero, Phys. Rev. Lett. 112, 201601 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.112.201601

[21] E. Zohar, M. Burrello, T. B. Wahl, and J. I. Cirac, Annals of Physics 363, 385 (2015).
https:/​/​doi.org/​10.1016/​j.aop.2015.10.009

[22] J. Haegeman, K. Van Acoleyen, N. Schuch, J. I. Cirac, and F. Verstraete, Phys. Rev. X 5, 011024 (2015).
https:/​/​doi.org/​10.1103/​PhysRevX.5.011024

[23] T. Pichler, M. Dalmonte, E. Rico, P. Zoller, and S. Montangero, Phys. Rev. X 6, 011023 (2016).
https:/​/​doi.org/​10.1103/​PhysRevX.6.011023

[24] E. Zohar and M. Burrello, New Journal of Physics 18, 043008 (2016).
https:/​/​doi.org/​10.1088/​1367-2630/​18/​4/​043008

[25] P. Silvi, E. Rico, M. Dalmonte, F. Tschirsich, and S. Montangero, Quantum 1, 9 (2017).
https:/​/​doi.org/​10.22331/​q-2017-04-25-9

[26] M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen, and S. Kühn, PoS LATTICE2018, 022 (2018).
https:/​/​doi.org/​10.22323/​1.334.0022

[27] G. Magnifico, D. Vodola, E. Ercolessi, S. P. Kumar, M. Müller, and A. Bermudez, Phys. Rev. B 100, 115152 (2019).
https:/​/​doi.org/​10.1103/​PhysRevB.100.115152

[28] T. Chanda, J. Zakrzewski, M. Lewenstein, and L. Tagliacozzo, Phys. Rev. Lett. 124, 180602 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.124.180602

[29] F. Tschirsich, S. Montangero, and M. Dalmonte, SciPost Phys. 6, 28 (2019).
https:/​/​doi.org/​10.21468/​SciPostPhys.6.3.028

[30] T. Felser, P. Silvi, M. Collura, and S. Montangero, Phys. Rev. X 10, 041040 (2020).
https:/​/​doi.org/​10.1103/​PhysRevX.10.041040

[31] D. Paulson, L. Dellantonio, J. F. Haase, A. Celi, A. Kan, A. Jena, C. Kokail, R. van Bijnen, K. Jansen, P. Zoller, and C. A. Muschik, (2020), arXiv:2008.09252 [quant-ph].
arXiv:2008.09252

[32] T. Byrnes and Y. Yamamoto, Phys. Rev. A 73, 022328 (2006).
https:/​/​doi.org/​10.1103/​PhysRevA.73.022328

[33] J. Preskill, arXiv:1811.10085.
arXiv:1811.10085

[34] M. C. Bañuls, R. Blatt, J. Catani, A. Celi, J. I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, et al., The European physical journal D 74, 1 (2020).
https:/​/​doi.org/​10.1140/​epjd/​e2020-100571-8

[35] M. C. Bañuls and K. Cichy, Rep. Prog. Phys. 83, 024401 (2020).

[36] W. P. Schleich, K. S. Ranade, C. Anton, M. Arndt, M. Aspelmeyer, et al., Appl. Phys. B 122, 130 (2016).
https:/​/​doi.org/​10.1007/​s00340-016-6353-8

[37] A. Acín, I. Bloch, H. Buhrman, T. Calarco, C. Eichler, et al., New J. Phys. 20, 080201 (2018).
https:/​/​doi.org/​10.1088/​1367-2630/​aad1ea

[38] E. A. Martinez, C. A. Muschik, P. Schindler, D. Nigg, A. Erhard, et al., Nature 534, 516 (2016).
https:/​/​doi.org/​10.1038/​nature18318

[39] N. Klco, E. F. Dumitrescu, A. J. McCaskey, T. D. Morris, R. C. Pooser, et al., Phys. Rev. A 98, 032331 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.032331

[40] C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, et al., Nature 569, 355 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-1177-4

[41] A. Mil, T. V. Zache, A. Hegde, A. Xia, R. P. Bhatt, et al., Science 367, 1128 (2020).
https:/​/​doi.org/​10.1126/​science.aaz5312

[42] B. Yang, H. Sun, R. Ott, H.-Y. Wang, T. V. Zache, J. C. Halimeh, Z.-S. Yuan, P. Hauke, and J.-W. Pan, Nature 587, 392 (2020).
https:/​/​doi.org/​10.1038/​s41586-020-2910-8

[43] C. Schweizer, F. Grusdt, M. Berngruber, L. Barbiero, E. Demler, et al., Nat. Phys. 15, 1168 (2019).
https:/​/​doi.org/​10.1038/​s41567-019-0649-7

[44] F. Görg, K. Sandholzer, J. Minguzzi, R. Desbuquois, M. Messer, et al., Nat. Phys. 15, 1161 (2019).
https:/​/​doi.org/​10.1038/​s41567-019-0615-4

[45] H. Weimer, M. Müller, I. Lesanovsky, P. Zoller, and H. P. Büchler, Nature Physics 6, 382 (2010).
https:/​/​doi.org/​10.1038/​nphys1614

[46] E. Zohar, J. I. Cirac, and B. Reznik, Phys. Rev. Lett. 109, 125302 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.109.125302

[47] L. Tagliacozzo, A. Celi, A. Zamora, and M. Lewenstein, Annals of Physics 330, 160 (2013a).
https:/​/​doi.org/​10.1016/​j.aop.2012.11.009

[48] L. Tagliacozzo, A. Celi, P. Orland, M. W. Mitchell, and M. Lewenstein, Nat. Com. 4, 2615 (2013b).
https:/​/​doi.org/​10.1038/​ncomms3615

[49] A. W. Glaetzle, M. Dalmonte, R. Nath, I. Rousochatzakis, R. Moessner, and P. Zoller, Phys. Rev. X 4, 041037 (2014).
https:/​/​doi.org/​10.1103/​PhysRevX.4.041037

[50] O. Dutta, L. Tagliacozzo, M. Lewenstein, and J. Zakrzewski, Phys. Rev. A 95, 053608 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.95.053608

[51] E. Zohar, A. Farace, B. Reznik, and J. I. Cirac, Phys. Rev. Lett. 118, 070501 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.118.070501

[52] D. C. Hackett, K. Howe, C. Hughes, W. Jay, E. T. Neil, and J. N. Simone, Phys. Rev. A 99, 062341 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.99.062341

[53] H. Lamm, S. Lawrence, and Y. Yamauchi (NuQS Collaboration), Phys. Rev. D 100, 034518 (2019).
https:/​/​doi.org/​10.1103/​PhysRevD.100.034518

[54] A. Celi, B. Vermersch, O. Viyuela, H. Pichler, M. D. Lukin, and P. Zoller, Phys. Rev. X 10, 021057 (2020).
https:/​/​doi.org/​10.1103/​PhysRevX.10.021057

[55] I. M. Georgescu, S. Ashhab, and F. Nori, Rev. Mod. Phys. 86, 153 (2014).
https:/​/​doi.org/​10.1103/​RevModPhys.86.153

[56] J. Preskill, Quantum 2, 79 (2018).
https:/​/​doi.org/​10.22331/​q-2018-08-06-79

[57] D. Horn, Phys. Lett. B 100, 149 (1981).
https:/​/​doi.org/​10.1016/​0370-2693(81)90763-2

[58] P. Orland and D. Rohrlich, Nucl. Phys. B 338, 647 (1990).
https:/​/​doi.org/​10.1016/​0550-3213(90)90646-U

[59] S. Chandrasekharan and U.-J. Wiese, Nucl. Phys. B 492, 455 (1997).
https:/​/​doi.org/​10.1016/​S0550-3213(97)80041-7

[60] D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988).
https:/​/​doi.org/​10.1103/​PhysRevLett.61.2376

[61] R. Moessner, S. L. Sondhi, and E. Fradkin, Phys. Rev. B 65, 024504 (2001).
https:/​/​doi.org/​10.1103/​PhysRevB.65.024504

[62] E. Fradkin, Field theories of condensed matter physics (Cambridge University Press, 2013).
https:/​/​doi.org/​10.1017/​CBO9781139015509

[63] S. Sachdev, Philos. T. R. Soc. A 374, 20150248 (2016).
https:/​/​doi.org/​10.1098/​rsta.2015.0248

[64] R. Brower, S. Chandrasekharan, and U.-J. Wiese, Phys. Rev. D 60, 094502 (1999).
https:/​/​doi.org/​10.1103/​PhysRevD.60.094502

[65] E. Zohar, J. I. Cirac, and B. Reznik, Phys. Rev. A 88, 023617 (2013).
https:/​/​doi.org/​10.1103/​PhysRevA.88.023617

[66] S. Kühn, J. I. Cirac, and M.-C. Bañuls, Phys. Rev. A 90, 042305 (2014).
https:/​/​doi.org/​10.1103/​PhysRevA.90.042305

[67] E. Ercolessi, P. Facchi, G. Magnifico, S. Pascazio, and F. V. Pepe, Phys. Rev. D 98, 074503 (2018).
https:/​/​doi.org/​10.1103/​PhysRevD.98.074503

[68] J. B. Kogut, Rev. Mod. Phys. 55, 775 (1983).
https:/​/​doi.org/​10.1103/​RevModPhys.55.775

[69] J. Stryker and D. Kaplan, PoS LATTICE2018, 227 (2019).
https:/​/​doi.org/​10.22323/​1.334.0227

[70] M. Creutz, Phys. Rev. D 21, 2308 (1980).
https:/​/​doi.org/​10.1103/​PhysRevD.21.2308

[71] J. Kogut and L. Susskind, Phys. Rev. D 11, 395 (1975).
https:/​/​doi.org/​10.1103/​PhysRevD.11.395

[72] O. Raviv, Y. Shamir, and B. Svetitsky, Phys. Rev. D 90, 014512 (2014).
https:/​/​doi.org/​10.1103/​PhysRevD.90.014512

[73] S. D. Drell, H. R. Quinn, B. Svetitsky, and M. Weinstein, Phys. Rev. D 19, 619 (1979).
https:/​/​doi.org/​10.1103/​PhysRevD.19.619

[74] H. R. Fiebig and R. M. Woloshyn, Phys. Rev. D 42, 3520 (1990).
https:/​/​doi.org/​10.1103/​PhysRevD.42.3520

[75] I. F. Herbut and B. H. Seradjeh, Phys. Rev. Lett. 91, 171601 (2003).
https:/​/​doi.org/​10.1103/​PhysRevLett.91.171601

[76] J. C. Halimeh, H. Lang, J. Mildenberger, Z. Jiang, and P. Hauke, arXiv:2007.00668.
arXiv:2007.00668

[77] H. D. Raedt, Comp. Phys. Rep. 7, 1 (1987).
https:/​/​doi.org/​10.1016/​0167-7977(87)90002-5

[78] C. J. Hamer, Z. Weihong, and J. Oitmaa, Phys. Rev. D 56, 55 (1997).
https:/​/​doi.org/​10.1103/​PhysRevD.56.55

[79] C. Muschik, M. Heyl, E. Martinez, T. Monz, P. Schindler, et al., New J. Phys. 19, 103020 (2017).
https:/​/​doi.org/​10.1088/​1367-2630/​aa89ab

[80] R. M. Reid, SIAM Review 39, 313 (1997).
https:/​/​doi.org/​10.1137/​S0036144595294801

[81] P. Jordan and E. P. Wigner, Z. Phys. 47, 631 (1928).
https:/​/​doi.org/​10.1007/​BF01331938

[82] C. V. Kraus, N. Schuch, F. Verstraete, and J. I. Cirac, Phys. Rev. A 81, 052338 (2010).
https:/​/​doi.org/​10.1103/​PhysRevA.81.052338

[83] E. Zohar and J. I. Cirac, Phys. Rev. B 98, 075119 (2018).
https:/​/​doi.org/​10.1103/​PhysRevB.98.075119

[84] J. Ambjørn and G. Semenoff, Phys. Let. B 226, 107 (1989).
https:/​/​doi.org/​10.1016/​0370-2693(89)90296-7

[85] D. Banerjee, M. Dalmonte, M. Müller, E. Rico, P. Stebler, et al., Phys. Rev. Lett. 109, 175302 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.109.175302

[86] V. Kasper, F. Hebenstreit, F. Jendrzejewski, M. K. Oberthaler, and J. Berges, 19, 023030 (2017).

[87] L. Barbiero, C. Schweizer, M. Aidelsburger, E. Demler, N. Goldman, and F. Grusdt, Science Advances 5 (2019).
https:/​/​doi.org/​10.1126/​sciadv.aav7444

[88] V. Kasper, G. Juzeliūnas, M. Lewenstein, F. Jendrzejewski, and E. Zohar, New Journal of Physics 22, 103027 (2020).
https:/​/​doi.org/​10.1088/​1367-2630/​abb961

[89] C. Senko, P. Richerme, J. Smith, A. Lee, I. Cohen, A. Retzker, and C. Monroe, Phys. Rev. X 5, 021026 (2015).
https:/​/​doi.org/​10.1103/​PhysRevX.5.021026

[90] J. Bender, P. Emonts, E. Zohar, and J. I. Cirac, Phys. Rev. Research 2, 043145 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.043145

[91] C. Laflamme, W. Evans, M. Dalmonte, U. Gerber, H. Mejía-Díaz, et al., Ann. Phys. 370, 117 (2016).
https:/​/​doi.org/​10.1016/​j.aop.2016.03.012

[92] J. Zhang, J. Unmuth-Yockey, J. Zeiher, A. Bazavov, S.-W. Tsai, and Y. Meurice, Phys. Rev. Lett. 121, 223201 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.121.223201

[93] Y. Meurice, Phys. Rev. D 102, 014506 (2020).
https:/​/​doi.org/​10.1103/​PhysRevD.102.014506

[94] A. Ammon, T. Hartung, K. Jansen, H. Leövey, and J. Volmer, Phys. Rev. D 94, 114508 (2016).
https:/​/​doi.org/​10.1103/​PhysRevD.94.114508

[95] A. Genz, J. Comput. Appl. Math. 157, 187 (2003).
https:/​/​doi.org/​10.1016/​S0377-0427(03)00413-8

[96] A. Alexandru, P. F. Bedaque, S. Harmalkar, H. Lamm, S. Lawrence, and N. C. Warrington (NuQS Collaboration), Phys. Rev. D 100, 114501 (2019).
https:/​/​doi.org/​10.1103/​PhysRevD.100.114501

[97] H. Lamm, S. Lawrence, and Y. Yamauchi (NuQS Collaboration), Phys. Rev. Research 2, 013272 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.013272

[98] R. M. Gray, Found. Trends Commun. Inf. Theory 2, 155 (2006).
https:/​/​doi.org/​10.1561/​0100000006

Cited by

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

[2] Erik J. Gustafson, Henry Lamm, and Judah Unmuth-Yockey, "Quantum mean estimation for lattice field theory", Physical Review D 107 11, 114511 (2023).

[3] Natalie Klco and Martin J. Savage, "Hierarchical qubit maps and hierarchically implemented quantum error correction", Physical Review A 104 6, 062425 (2021).

[4] 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).

[5] Anthony N. Ciavarella, Stephan Caspar, Hersh Singh, Martin J. Savage, and Pavel Lougovski, "Simulating Heisenberg interactions in the Ising model with strong drive fields", Physical Review A 108 4, 042216 (2023).

[6] 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).

[7] Saurabh V. Kadam, Indrakshi Raychowdhury, and Jesse R. Stryker, "Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks", Physical Review D 107 9, 094513 (2023).

[8] 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).

[9] 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).

[10] Lento Nagano, Alexander Miessen, Tamiya Onodera, Ivano Tavernelli, Francesco Tacchino, and Koji Terashi, "Quantum data learning for quantum simulations in high-energy physics", Physical Review Research 5 4, 043250 (2023).

[11] 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).

[12] Julian Bender, Patrick Emonts, and J. Ignacio Cirac, "Variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: A study of (2+1) -dimensional compact QED with dynamical fermions at finite density", Physical Review Research 5 4, 043128 (2023).

[13] 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).

[14] Tomohiro Hashizume, Jad Halimeh, Philipp Hauke, and Debasish Banerjee, "Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d", SciPost Physics 13 2, 017 (2022).

[15] 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).

[16] Giuseppe Clemente, Arianna Crippa, and Karl Jansen, "Strategies for the determination of the running coupling of ( 2+1 )-dimensional QED with quantum computing", Physical Review D 106 11, 114511 (2022).

[17] Zachary Parks, Arnaud Carignan-Dugas, Erik Gustafson, Yannick Meurice, and Patrick Dreher, "Applying the noiseless extrapolation error mitigation protocol to calculate real-time quantum field theory scattering phase shifts", Physical Review D 109 1, 014505 (2024).

[18] Kevissen Sellapillay, Pablo Arrighi, and Giuseppe Di Molfetta, "A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limits", Scientific Reports 12 1, 2198 (2022).

[19] Marcela Carena, Henry Lamm, Ying-Ying Li, and Wanqiang Liu, "Improved Hamiltonians for Quantum Simulations of Gauge Theories", Physical Review Letters 129 5, 051601 (2022).

[20] Timo Jakobs, Marco Garofalo, Tobias Hartung, Karl Jansen, Johann Ostmeyer, Dominik Rolfes, Simone Romiti, and Carsten Urbach, "Canonical momenta in digitized Su(2) lattice gauge theory: definition and free theory", The European Physical Journal C 83 7, 669 (2023).

[21] Nathanaël Eon, Giuseppe Di Molfetta, Giuseppe Magnifico, and Pablo Arrighi, "A relativistic discrete spacetime formulation of 3+1 QED", Quantum 7, 1179 (2023).

[22] Michael Fromm, Owe Philipsen, and Christopher Winterowd, "Dihedral lattice gauge theories on a quantum annealer", EPJ Quantum Technology 10 1, 31 (2023).

[23] 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).

[24] 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).

[25] 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).

[26] 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).

[27] Giuseppe Magnifico, Timo Felser, Pietro Silvi, and Simone Montangero, "Lattice quantum electrodynamics in (3+1)-dimensions at finite density with tensor networks", Nature Communications 12 1, 3600 (2021).

[28] 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).

[29] Christian W. Bauer and Dorota M. Grabowska, "Efficient representation for simulating U(1) gauge theories on digital quantum computers at all values of the coupling", Physical Review D 107 3, L031503 (2023).

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

[31] 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).

[32] Erik J. Gustafson, Henry Lamm, Felicity Lovelace, and Damian Musk, "Primitive quantum gates for an SU(2) discrete subgroup: Binary tetrahedral", Physical Review D 106 11, 114501 (2022).

[33] Bin Xu and Wei Xue, "( 3+1 )-dimensional Schwinger pair production with quantum computers", Physical Review D 106 11, 116007 (2022).

[34] Lena Funcke, Tobias Hartung, Karl Jansen, Stefan Kuhn, Manuel Schneider, and Paolo Stornati, 2021 IEEE International Conference on Web Services (ICWS) 693 (2021) ISBN:978-1-6654-1681-8.

[35] Guy Pardo, Tomer Greenberg, Aryeh Fortinsky, Nadav Katz, and Erez Zohar, "Resource-efficient quantum simulation of lattice gauge theories in arbitrary dimensions: Solving for Gauss's law and fermion elimination", Physical Review Research 5 2, 023077 (2023).

[36] Erik J. Gustafson and Henry Lamm, "Toward quantum simulations ofZ2gauge theory without state preparation", Physical Review D 103 5, 054507 (2021).

[37] Anthony N. Ciavarella, Stephan Caspar, Hersh Singh, and Martin J. Savage, "Preparation for quantum simulation of the (1+1) -dimensional O(3) nonlinear σ model using cold atoms", Physical Review A 107 4, 042404 (2023).

[38] Hersh Singh, "Qubit regularized O(N) nonlinear sigma models", Physical Review D 105 11, 114509 (2022).

[39] 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).

[40] 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).

[41] Luca Lumia, Pietro Torta, Glen B. Mbeng, Giuseppe E. Santoro, Elisa Ercolessi, Michele Burrello, and Matteo M. Wauters, "Two-Dimensional Z2 Lattice Gauge Theory on a Near-Term Quantum Simulator: Variational Quantum Optimization, Confinement, and Topological Order", PRX Quantum 3 2, 020320 (2022).

[42] Yasar Y. Atas, Jinglei Zhang, Randy Lewis, Amin Jahanpour, Jan F. Haase, and Christine A. Muschik, "SU(2) hadrons on a quantum computer via a variational approach", Nature Communications 12 1, 6499 (2021).

[43] Torsten V. Zache, Daniel González-Cuadra, and Peter Zoller, "Fermion-qudit quantum processors for simulating lattice gauge theories with matter", Quantum 7, 1140 (2023).

[44] Angus Kan, Lena Funcke, Stefan Kühn, Luca Dellantonio, Jinglei Zhang, Jan F. Haase, Christine A. Muschik, and Karl Jansen, "Investigating a (3+1)D topological θ -term in the Hamiltonian formulation of lattice gauge theories for quantum and classical simulations", Physical Review D 104 3, 034504 (2021).

[45] Shachar Ashkenazi and Erez Zohar, "Duality as a feasible physical transformation for quantum simulation", Physical Review A 105 2, 022431 (2022).

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

[47] Jiří Minář, Bart van Voorden, and Kareljan Schoutens, "Kink Dynamics and Quantum Simulation of Supersymmetric Lattice Hamiltonians", Physical Review Letters 128 5, 050504 (2022).

[48] Erez Zohar, "Quantum simulation of lattice gauge theories in more than one space dimension—requirements, challenges and methods", Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380 2216, 20210069 (2022).

[49] Mendel Nguyen and Hersh Singh, "Lattice regularizations of θ vacua: Anomalies and qubit models", Physical Review D 107 1, 014507 (2023).

[50] C. S. Chisholm, A. Frölian, E. Neri, R. Ramos, L. Tarruell, and A. Celi, "Encoding a one-dimensional topological gauge theory in a Raman-coupled Bose-Einstein condensate", Physical Review Research 4 4, 043088 (2022).

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

[52] L. Funcke, T. Hartung, K. Jansen, S. Kühn, M. Schneider, P. Stornati, and X. Wang, "Towards quantum simulations in particle physics and beyond on noisy intermediate-scale quantum devices", Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380 2216, 20210062 (2022).

[53] Jorge Miguel-Ramiro, Zheng Shi, Luca Dellantonio, Albie Chan, Christine A. Muschik, and Wolfgang Dür, "Superposed Quantum Error Mitigation", Physical Review Letters 131 23, 230601 (2023).

[54] 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).

[55] Christian W. Bauer, Benjamin Nachman, and Marat Freytsis, "Simulating Collider Physics on Quantum Computers Using Effective Field Theories", Physical Review Letters 127 21, 212001 (2021).

[56] Nouman Butt, Xiao-Yong Jin, James C. Osborn, and Zain H. Saleem, "Moving from continuous to discrete symmetry in the 2D XY model", Physical Review D 108 7, 074511 (2023).

[57] 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).

[58] R. Ott, T. V. Zache, F. Jendrzejewski, and J. Berges, "Scalable Cold-Atom Quantum Simulator for Two-Dimensional QED", Physical Review Letters 127 13, 130504 (2021).

[59] 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).

[60] Jinglei Zhang, Ryan Ferguson, Stefan Kühn, Jan F. Haase, C.M. Wilson, Karl Jansen, and Christine A. Muschik, "Simulating gauge theories with variational quantum eigensolvers in superconducting microwave cavities", Quantum 7, 1148 (2023).

[61] 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).

[62] 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).

[63] Ariel Shlosberg, Andrew J. Jena, Priyanka Mukhopadhyay, Jan F. Haase, Felix Leditzky, and Luca Dellantonio, "Adaptive estimation of quantum observables", Quantum 7, 906 (2023).

[64] R. R. Ferguson, L. Dellantonio, A. Al Balushi, K. Jansen, W. Dür, and C. A. Muschik, "Measurement-Based Variational Quantum Eigensolver", Physical Review Letters 126 22, 220501 (2021).

[65] Leon Hostetler, Jin Zhang, Ryo Sakai, Judah Unmuth-Yockey, Alexei Bazavov, and Yannick Meurice, "Clock model interpolation and symmetry breaking in O(2) models", Physical Review D 104 5, 054505 (2021).

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

[67] Marcela Carena, Erik J. Gustafson, Henry Lamm, Ying-Ying Li, and Wanqiang Liu, "Gauge theory couplings on anisotropic lattices", Physical Review D 106 11, 114504 (2022).

[68] 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).

[69] 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).

[70] David B. Kaplan and Jesse R. Stryker, "Gauss's law, duality, and the Hamiltonian formulation of U(1) lattice gauge theory", Physical Review D 102 9, 094515 (2020).

[71] Julian Bender and Erez Zohar, "Gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations", Physical Review D 102 11, 114517 (2020).

[72] Simon Catterall, Roni Harnik, Veronika E. Hubeny, Christian W. Bauer, Asher Berlin, Zohreh Davoudi, Thomas Faulkner, Thomas Hartman, Matthew Headrick, Yonatan F. Kahn, Henry Lamm, Yannick Meurice, Surjeet Rajendran, Mukund Rangamani, and Brian Swingle, "Report of the Snowmass 2021 Theory Frontier Topical Group on Quantum Information Science", arXiv:2209.14839, (2022).

[73] Christian W. Bauer and Dorota M. Grabowska, "Efficient Representation for Simulating U(1) Gauge Theories on Digital Quantum Computers at All Values of the Coupling", arXiv:2111.08015, (2021).

[74] Lena Funcke, Tobias Hartung, Karl Jansen, Stefan Kühn, and Paolo Stornati, "Dimensional Expressivity Analysis of Parametric Quantum Circuits", Quantum 5, 422 (2021).

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

[76] Matteo Turco, Gonçalo M. Quinta, João Seixas, and Yasser Omar, "Towards Quantum Simulation of Bound States Scattering", arXiv:2305.07692, (2023).

[77] Erik J. Gustafson, Henry Lamm, and Felicity Lovelace, "Primitive Quantum Gates for an $SU(2)$ Discrete Subgroup: Binary Octahedral", arXiv:2312.10285, (2023).

[78] Saurabh V. Kadam, "Theoretical Developments in Lattice Gauge Theory for Applications in Double-beta Decay Processes and Quantum Simulation", arXiv:2312.00780, (2023).

[79] Christopher Kane, Dorota M. Grabowska, Benjamin Nachman, and Christian W. Bauer, "Efficient quantum implementation of 2+1 U(1) lattice gauge theories with Gauss law constraints", arXiv:2211.10497, (2022).

[80] Dorota M. Grabowska, Christopher Kane, Benjamin Nachman, and Christian W. Bauer, "Overcoming exponential scaling with system size in Trotter-Suzuki implementations of constrained Hamiltonians: 2+1 U(1) lattice gauge theories", arXiv:2208.03333, (2022).

[81] Natalie Klco, D. H. Beck, and Martin J. Savage, "Entanglement Structures in Quantum Field Theories: Negativity Cores and Bound Entanglement in the Vacuum", arXiv:2110.10736, (2021).

[82] Albie Chan, Zheng Shi, Luca Dellantonio, Wolfgang Dür, and Christine A. Muschik, "Hybrid variational quantum eigensolvers: merging computational models", arXiv:2305.19200, (2023).

[83] Christopher F. Kane, Niladri Gomes, and Michael Kreshchuk, "Nearly-optimal state preparation for quantum simulations of lattice gauge theories", arXiv:2310.13757, (2023).

[84] Masanori Hanada, Junyu Liu, Enrico Rinaldi, and Masaki Tezuka, "Estimating truncation effects of quantum bosonic systems using sampling algorithms", Machine Learning: Science and Technology 4 4, 045021 (2023).

[85] S. V. Kadam, I. Raychowdhury, and J. Stryker, "Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks", The 39th International Symposium on Lattice Field Theory, 373 (2023).

[86] Julian Bender and Erez Zohar, "A gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations", arXiv:2008.01349, (2020).

[87] Jens Nyhegn, Chia-Min Chung, and Michele Burrello, "Z<SUB>N</SUB> lattice gauge theory in a ladder geometry", Physical Review Research 3 1, 013133 (2021).

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

[89] Erik J. Gustafson, "Stout Smearing on a Quantum Computer", arXiv:2211.05607, (2022).

[90] Emanuele Mendicelli, "Investigating how to simulate lattice gauge theories on a quantum computer", arXiv:2308.15421, (2023).

[91] Zachary Parks, Arnaud Carignan-Dugas, Erik Gustafson, Yannick Meurice, and Patrick Dreher, "Applying NOX Error Mitigation Protocols to Calculate Real-time Quantum Field Theory Scattering Phase Shifts", arXiv:2212.05333, (2022).

[92] 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).

[93] Pierpaolo Fontana, Joao C. Pinto Barros, and Andrea Trombettoni, "Reformulation of gauge theories in terms of gauge invariant fields", Annals of Physics 436, 168683 (2022).

[94] Pierpaolo Fontana, Joao C. Pinto Barros, and Andrea Trombettoni, "Reformulation of gauge theories in terms of gauge invariant fields", arXiv:2008.12973, (2020).

The above citations are from Crossref's cited-by service (last updated successfully 2024-02-26 08:48:47) and SAO/NASA ADS (last updated successfully 2024-02-26 08:48:48). The list may be incomplete as not all publishers provide suitable and complete citation data.