{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T04:44:58Z","timestamp":1772599498308,"version":"3.50.1"},"reference-count":98,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2021,2,4]],"date-time":"2021-02-04T00:00:00Z","timestamp":1612396800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>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 <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>2<\/mml:mn><mml:mo>+<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math> 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.<\/jats:p>","DOI":"10.22331\/q-2021-02-04-393","type":"journal-article","created":{"date-parts":[[2021,7,5]],"date-time":"2021-07-05T21:20:36Z","timestamp":1625520036000},"page":"393","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":114,"title":["A resource efficient approach for quantum and classical simulations of gauge theories in particle physics"],"prefix":"10.22331","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1126-8216","authenticated-orcid":false,"given":"Jan F.","family":"Haase","sequence":"first","affiliation":[{"name":"Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1"},{"name":"Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1914-6539","authenticated-orcid":false,"given":"Luca","family":"Dellantonio","sequence":"additional","affiliation":[{"name":"Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1"},{"name":"Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4939-084X","authenticated-orcid":false,"given":"Alessio","family":"Celi","sequence":"additional","affiliation":[{"name":"Departament de F\u00edsica, Universitat Aut\u00f2noma de Barcelona, E-08193 Bellaterra, Spain"},{"name":"Center for Quantum Physics, Faculty of Mathematics, Computer Science and Physics, University of Innsbruck, Innsbruck A-6020, Austria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2522-4046","authenticated-orcid":false,"given":"Danny","family":"Paulson","sequence":"additional","affiliation":[{"name":"Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1"},{"name":"Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1"}]},{"given":"Angus","family":"Kan","sequence":"additional","affiliation":[{"name":"Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1"},{"name":"Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1574-7591","authenticated-orcid":false,"given":"Karl","family":"Jansen","sequence":"additional","affiliation":[{"name":"NIC, DESY, Platanenallee 6, D-15738 Zeuthen, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4599-5107","authenticated-orcid":false,"given":"Christine A.","family":"Muschik","sequence":"additional","affiliation":[{"name":"Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1"},{"name":"Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1"},{"name":"Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada, N2L 2Y5"}]}],"member":"9598","published-online":{"date-parts":[[2021,2,4]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"W. N. Cottingham and D. A. Greenwood, An Introduction to the Standard Model of Particle Physics, 2nd ed. (Cambridge University Press, 2007).","DOI":"10.1017\/CBO9780511791406"},{"key":"1","doi-asserted-by":"publisher","unstructured":"G. Altarelli, Collider Physics within the Standard Model, 1st ed., Lecture Notes in Physics, Vol. 937 (Springer International Publishing, 2017).","DOI":"10.1007\/978-3-319-51920-3"},{"key":"2","doi-asserted-by":"crossref","unstructured":"M. E. Peskin and D. V. Schroeder, An introduction to quantum field theory (CRC press, 2018).","DOI":"10.1201\/9780429503559"},{"key":"3","unstructured":"G. Altarelli, Frascati Phys. Ser. 58, 102 (2014)."},{"key":"4","doi-asserted-by":"publisher","unstructured":"M. J. Veltman, Facts and Mysteries in Elementary Particle Physics (World Scientific, 2018).","DOI":"10.1142\/10904"},{"key":"5","doi-asserted-by":"publisher","unstructured":"T. DeGrand and C. E. Detar, Lattice methods for quantum chromodynamics (World Scientific, 2006).","DOI":"10.1142\/6065"},{"key":"6","doi-asserted-by":"publisher","unstructured":"H. J. Rothe, Lattice Gauge Theories (World Scientific, 1992).","DOI":"10.1142\/8229"},{"key":"7","doi-asserted-by":"publisher","unstructured":"C. Gattringer and C. B. Lang, Quantum chromodynamics on the lattice, Vol. 788 (Springer, Berlin, 2010).","DOI":"10.1007\/978-3-642-01850-3"},{"key":"8","doi-asserted-by":"publisher","unstructured":"K. G. Wilson, Phys. Rev. D 10, 2445 (1974).","DOI":"10.1103\/PhysRevD.10.2445"},{"key":"9","doi-asserted-by":"publisher","unstructured":"S. Durr et al., Science 322, 1224 (2008).","DOI":"10.1126\/science.1163233"},{"key":"10","doi-asserted-by":"publisher","unstructured":"M. Constantinou, PoS CD15, 009 (2016).","DOI":"10.22323\/1.253.0009"},{"key":"11","doi-asserted-by":"publisher","unstructured":"A. Prokudin, K. Cichy, and M. Constantinou, Advances in High Energy Physics 2019, 3036904 (2019).","DOI":"10.1155\/2019\/3036904"},{"key":"12","doi-asserted-by":"publisher","unstructured":"H. B. Meyer and H. Wittig, Prog. Part. Nucl. Phys. 104, 46 (2019).","DOI":"10.1016\/j.ppnp.2018.09.001"},{"key":"13","doi-asserted-by":"publisher","unstructured":"A. Juttner, PoS LATTICE 2015, 006 (2016).","DOI":"10.22323\/1.251.0006"},{"key":"14","doi-asserted-by":"publisher","unstructured":"M. Troyer and U.-J. Wiese, Phys. Rev. Lett. 94, 170201 (2005).","DOI":"10.1103\/PhysRevLett.94.170201"},{"key":"15","doi-asserted-by":"publisher","unstructured":"M. C. Ba\u00f1uls and K. Cichy, Rept. Prog. Phys. 83, 024401 (2020).","DOI":"10.1088\/1361-6633\/ab6311"},{"key":"16","doi-asserted-by":"publisher","unstructured":"M. C. Ba\u00f1uls, K. Cichy, J. I. Cirac, K. Jansen, and S. K\u00fchn, Phys. Rev. Lett. 118, 071601 (2017).","DOI":"10.1103\/PhysRevLett.118.071601"},{"key":"17","doi-asserted-by":"publisher","unstructured":"T. Sugihara, J. High Energy Phys. 2005, 022 (2005).","DOI":"10.1088\/1126-6708\/2005\/07\/022"},{"key":"18","doi-asserted-by":"crossref","unstructured":"L. Tagliacozzo, A. Celi, and M. Lewenstein, Phys. Rev. X 4, 041024 (2014).","DOI":"10.1103\/PhysRevX.4.041024"},{"key":"19","doi-asserted-by":"publisher","unstructured":"E. Rico, T. Pichler, M. Dalmonte, P. Zoller, and S. Montangero, Phys. Rev. Lett. 112, 201601 (2014).","DOI":"10.1103\/PhysRevLett.112.201601"},{"key":"20","doi-asserted-by":"publisher","unstructured":"E. Zohar, M. Burrello, T. B. Wahl, and J. I. Cirac, Annals of Physics 363, 385 (2015).","DOI":"10.1016\/j.aop.2015.10.009"},{"key":"21","doi-asserted-by":"publisher","unstructured":"J. Haegeman, K. Van Acoleyen, N. Schuch, J. I. Cirac, and F. Verstraete, Phys. Rev. X 5, 011024 (2015).","DOI":"10.1103\/PhysRevX.5.011024"},{"key":"22","doi-asserted-by":"publisher","unstructured":"T. Pichler, M. Dalmonte, E. Rico, P. Zoller, and S. Montangero, Phys. Rev. X 6, 011023 (2016).","DOI":"10.1103\/PhysRevX.6.011023"},{"key":"23","doi-asserted-by":"publisher","unstructured":"E. Zohar and M. Burrello, New Journal of Physics 18, 043008 (2016).","DOI":"10.1088\/1367-2630\/18\/4\/043008"},{"key":"24","doi-asserted-by":"publisher","unstructured":"P. Silvi, E. Rico, M. Dalmonte, F. Tschirsich, and S. Montangero, Quantum 1, 9 (2017).","DOI":"10.22331\/q-2017-04-25-9"},{"key":"25","doi-asserted-by":"publisher","unstructured":"M. C. Ba\u00f1uls, K. Cichy, J. I. Cirac, K. Jansen, and S. K\u00fchn, PoS LATTICE2018, 022 (2018).","DOI":"10.22323\/1.334.0022"},{"key":"26","doi-asserted-by":"publisher","unstructured":"G. Magnifico, D. Vodola, E. Ercolessi, S. P. Kumar, M. M\u00fcller, and A. Bermudez, Phys. Rev. B 100, 115152 (2019).","DOI":"10.1103\/PhysRevB.100.115152"},{"key":"27","doi-asserted-by":"publisher","unstructured":"T. Chanda, J. Zakrzewski, M. Lewenstein, and L. Tagliacozzo, Phys. Rev. Lett. 124, 180602 (2020).","DOI":"10.1103\/PhysRevLett.124.180602"},{"key":"28","doi-asserted-by":"publisher","unstructured":"F. Tschirsich, S. Montangero, and M. Dalmonte, SciPost Phys. 6, 28 (2019).","DOI":"10.21468\/SciPostPhys.6.3.028"},{"key":"29","doi-asserted-by":"publisher","unstructured":"T. Felser, P. Silvi, M. Collura, and S. Montangero, Phys. Rev. X 10, 041040 (2020).","DOI":"10.1103\/PhysRevX.10.041040"},{"key":"30","unstructured":"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]."},{"key":"31","doi-asserted-by":"publisher","unstructured":"T. Byrnes and Y. Yamamoto, Phys. Rev. A 73, 022328 (2006).","DOI":"10.1103\/PhysRevA.73.022328"},{"key":"32","unstructured":"J. Preskill, arXiv:1811.10085."},{"key":"33","doi-asserted-by":"publisher","unstructured":"M. C. Ba\u00f1uls, 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).","DOI":"10.1140\/epjd\/e2020-100571-8"},{"key":"34","doi-asserted-by":"crossref","unstructured":"M. C. Ba\u00f1uls and K. Cichy, Rep. Prog. Phys. 83, 024401 (2020).","DOI":"10.1088\/1361-6633\/ab6311"},{"key":"35","doi-asserted-by":"publisher","unstructured":"W. P. Schleich, K. S. Ranade, C. Anton, M. Arndt, M. Aspelmeyer, et al., Appl. Phys. B 122, 130 (2016).","DOI":"10.1007\/s00340-016-6353-8"},{"key":"36","doi-asserted-by":"publisher","unstructured":"A. Ac\u00edn, I. Bloch, H. Buhrman, T. Calarco, C. Eichler, et al., New J. Phys. 20, 080201 (2018).","DOI":"10.1088\/1367-2630\/aad1ea"},{"key":"37","doi-asserted-by":"publisher","unstructured":"E. A. Martinez, C. A. Muschik, P. Schindler, D. Nigg, A. Erhard, et al., Nature 534, 516 (2016).","DOI":"10.1038\/nature18318"},{"key":"38","doi-asserted-by":"publisher","unstructured":"N. Klco, E. F. Dumitrescu, A. J. McCaskey, T. D. Morris, R. C. Pooser, et al., Phys. Rev. A 98, 032331 (2018).","DOI":"10.1103\/PhysRevA.98.032331"},{"key":"39","doi-asserted-by":"publisher","unstructured":"C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, et al., Nature 569, 355 (2019).","DOI":"10.1038\/s41586-019-1177-4"},{"key":"40","doi-asserted-by":"publisher","unstructured":"A. Mil, T. V. Zache, A. Hegde, A. Xia, R. P. Bhatt, et al., Science 367, 1128 (2020).","DOI":"10.1126\/science.aaz5312"},{"key":"41","doi-asserted-by":"publisher","unstructured":"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).","DOI":"10.1038\/s41586-020-2910-8"},{"key":"42","doi-asserted-by":"publisher","unstructured":"C. Schweizer, F. Grusdt, M. Berngruber, L. Barbiero, E. Demler, et al., Nat. Phys. 15, 1168 (2019).","DOI":"10.1038\/s41567-019-0649-7"},{"key":"43","doi-asserted-by":"publisher","unstructured":"F. G\u00f6rg, K. Sandholzer, J. Minguzzi, R. Desbuquois, M. Messer, et al., Nat. Phys. 15, 1161 (2019).","DOI":"10.1038\/s41567-019-0615-4"},{"key":"44","doi-asserted-by":"publisher","unstructured":"H. Weimer, M. M\u00fcller, I. Lesanovsky, P. Zoller, and H. P. B\u00fcchler, Nature Physics 6, 382 (2010).","DOI":"10.1038\/nphys1614"},{"key":"45","doi-asserted-by":"publisher","unstructured":"E. Zohar, J. I. Cirac, and B. Reznik, Phys. Rev. Lett. 109, 125302 (2012).","DOI":"10.1103\/PhysRevLett.109.125302"},{"key":"46","doi-asserted-by":"publisher","unstructured":"L. Tagliacozzo, A. Celi, A. Zamora, and M. Lewenstein, Annals of Physics 330, 160 (2013a).","DOI":"10.1016\/j.aop.2012.11.009"},{"key":"47","doi-asserted-by":"publisher","unstructured":"L. Tagliacozzo, A. Celi, P. Orland, M. W. Mitchell, and M. Lewenstein, Nat. Com. 4, 2615 (2013b).","DOI":"10.1038\/ncomms3615"},{"key":"48","doi-asserted-by":"publisher","unstructured":"A. W. Glaetzle, M. Dalmonte, R. Nath, I. Rousochatzakis, R. Moessner, and P. Zoller, Phys. Rev. X 4, 041037 (2014).","DOI":"10.1103\/PhysRevX.4.041037"},{"key":"49","doi-asserted-by":"publisher","unstructured":"O. Dutta, L. Tagliacozzo, M. Lewenstein, and J. Zakrzewski, Phys. Rev. A 95, 053608 (2017).","DOI":"10.1103\/PhysRevA.95.053608"},{"key":"50","doi-asserted-by":"publisher","unstructured":"E. Zohar, A. Farace, B. Reznik, and J. I. Cirac, Phys. Rev. Lett. 118, 070501 (2017).","DOI":"10.1103\/PhysRevLett.118.070501"},{"key":"51","doi-asserted-by":"publisher","unstructured":"D. C. Hackett, K. Howe, C. Hughes, W. Jay, E. T. Neil, and J. N. Simone, Phys. Rev. A 99, 062341 (2019).","DOI":"10.1103\/PhysRevA.99.062341"},{"key":"52","doi-asserted-by":"publisher","unstructured":"H. Lamm, S. Lawrence, and Y. Yamauchi (NuQS Collaboration), Phys. Rev. D 100, 034518 (2019).","DOI":"10.1103\/PhysRevD.100.034518"},{"key":"53","doi-asserted-by":"publisher","unstructured":"A. Celi, B. Vermersch, O. Viyuela, H. Pichler, M. D. Lukin, and P. Zoller, Phys. Rev. X 10, 021057 (2020).","DOI":"10.1103\/PhysRevX.10.021057"},{"key":"54","doi-asserted-by":"publisher","unstructured":"I. M. Georgescu, S. Ashhab, and F. Nori, Rev. Mod. Phys. 86, 153 (2014).","DOI":"10.1103\/RevModPhys.86.153"},{"key":"55","doi-asserted-by":"publisher","unstructured":"J. Preskill, Quantum 2, 79 (2018).","DOI":"10.22331\/q-2018-08-06-79"},{"key":"56","doi-asserted-by":"publisher","unstructured":"D. Horn, Phys. Lett. B 100, 149 (1981).","DOI":"10.1016\/0370-2693(81)90763-2"},{"key":"57","doi-asserted-by":"publisher","unstructured":"P. Orland and D. Rohrlich, Nucl. Phys. B 338, 647 (1990).","DOI":"10.1016\/0550-3213(90)90646-U"},{"key":"58","doi-asserted-by":"publisher","unstructured":"S. Chandrasekharan and U.-J. Wiese, Nucl. Phys. B 492, 455 (1997).","DOI":"10.1016\/S0550-3213(97)80041-7"},{"key":"59","doi-asserted-by":"publisher","unstructured":"D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988).","DOI":"10.1103\/PhysRevLett.61.2376"},{"key":"60","doi-asserted-by":"publisher","unstructured":"R. Moessner, S. L. Sondhi, and E. Fradkin, Phys. Rev. B 65, 024504 (2001).","DOI":"10.1103\/PhysRevB.65.024504"},{"key":"61","doi-asserted-by":"publisher","unstructured":"E. Fradkin, Field theories of condensed matter physics (Cambridge University Press, 2013).","DOI":"10.1017\/CBO9781139015509"},{"key":"62","doi-asserted-by":"publisher","unstructured":"S. Sachdev, Philos. T. R. Soc. A 374, 20150248 (2016).","DOI":"10.1098\/rsta.2015.0248"},{"key":"63","doi-asserted-by":"publisher","unstructured":"R. Brower, S. Chandrasekharan, and U.-J. Wiese, Phys. Rev. D 60, 094502 (1999).","DOI":"10.1103\/PhysRevD.60.094502"},{"key":"64","doi-asserted-by":"publisher","unstructured":"E. Zohar, J. I. Cirac, and B. Reznik, Phys. Rev. A 88, 023617 (2013).","DOI":"10.1103\/PhysRevA.88.023617"},{"key":"65","doi-asserted-by":"publisher","unstructured":"S. K\u00fchn, J. I. Cirac, and M.-C. Ba\u00f1uls, Phys. Rev. A 90, 042305 (2014).","DOI":"10.1103\/PhysRevA.90.042305"},{"key":"66","doi-asserted-by":"publisher","unstructured":"E. Ercolessi, P. Facchi, G. Magnifico, S. Pascazio, and F. V. Pepe, Phys. Rev. D 98, 074503 (2018).","DOI":"10.1103\/PhysRevD.98.074503"},{"key":"67","doi-asserted-by":"publisher","unstructured":"J. B. Kogut, Rev. Mod. Phys. 55, 775 (1983).","DOI":"10.1103\/RevModPhys.55.775"},{"key":"68","doi-asserted-by":"publisher","unstructured":"J. Stryker and D. Kaplan, PoS LATTICE2018, 227 (2019).","DOI":"10.22323\/1.334.0227"},{"key":"69","doi-asserted-by":"publisher","unstructured":"M. Creutz, Phys. Rev. D 21, 2308 (1980).","DOI":"10.1103\/PhysRevD.21.2308"},{"key":"70","doi-asserted-by":"publisher","unstructured":"J. Kogut and L. Susskind, Phys. Rev. D 11, 395 (1975).","DOI":"10.1103\/PhysRevD.11.395"},{"key":"71","doi-asserted-by":"publisher","unstructured":"O. Raviv, Y. Shamir, and B. Svetitsky, Phys. Rev. D 90, 014512 (2014).","DOI":"10.1103\/PhysRevD.90.014512"},{"key":"72","doi-asserted-by":"publisher","unstructured":"S. D. Drell, H. R. Quinn, B. Svetitsky, and M. Weinstein, Phys. Rev. D 19, 619 (1979).","DOI":"10.1103\/PhysRevD.19.619"},{"key":"73","doi-asserted-by":"publisher","unstructured":"H. R. Fiebig and R. M. Woloshyn, Phys. Rev. D 42, 3520 (1990).","DOI":"10.1103\/PhysRevD.42.3520"},{"key":"74","doi-asserted-by":"publisher","unstructured":"I. F. Herbut and B. H. Seradjeh, Phys. Rev. Lett. 91, 171601 (2003).","DOI":"10.1103\/PhysRevLett.91.171601"},{"key":"75","unstructured":"J. C. Halimeh, H. Lang, J. Mildenberger, Z. Jiang, and P. Hauke, arXiv:2007.00668."},{"key":"76","doi-asserted-by":"publisher","unstructured":"H. D. Raedt, Comp. Phys. Rep. 7, 1 (1987).","DOI":"10.1016\/0167-7977(87)90002-5"},{"key":"77","doi-asserted-by":"publisher","unstructured":"C. J. Hamer, Z. Weihong, and J. Oitmaa, Phys. Rev. D 56, 55 (1997).","DOI":"10.1103\/PhysRevD.56.55"},{"key":"78","doi-asserted-by":"publisher","unstructured":"C. Muschik, M. Heyl, E. Martinez, T. Monz, P. Schindler, et al., New J. Phys. 19, 103020 (2017).","DOI":"10.1088\/1367-2630\/aa89ab"},{"key":"79","doi-asserted-by":"publisher","unstructured":"R. M. Reid, SIAM Review 39, 313 (1997).","DOI":"10.1137\/S0036144595294801"},{"key":"80","doi-asserted-by":"publisher","unstructured":"P. Jordan and E. P. Wigner, Z. Phys. 47, 631 (1928).","DOI":"10.1007\/BF01331938"},{"key":"81","doi-asserted-by":"publisher","unstructured":"C. V. Kraus, N. Schuch, F. Verstraete, and J. I. Cirac, Phys. Rev. A 81, 052338 (2010).","DOI":"10.1103\/PhysRevA.81.052338"},{"key":"82","doi-asserted-by":"publisher","unstructured":"E. Zohar and J. I. Cirac, Phys. Rev. B 98, 075119 (2018).","DOI":"10.1103\/PhysRevB.98.075119"},{"key":"83","doi-asserted-by":"publisher","unstructured":"J. Ambj\u00f8rn and G. Semenoff, Phys. Let. B 226, 107 (1989).","DOI":"10.1016\/0370-2693(89)90296-7"},{"key":"84","doi-asserted-by":"publisher","unstructured":"D. Banerjee, M. Dalmonte, M. M\u00fcller, E. Rico, P. Stebler, et al., Phys. Rev. Lett. 109, 175302 (2012).","DOI":"10.1103\/PhysRevLett.109.175302"},{"key":"85","doi-asserted-by":"crossref","unstructured":"V. Kasper, F. Hebenstreit, F. Jendrzejewski, M. K. Oberthaler, and J. Berges, 19, 023030 (2017).","DOI":"10.1088\/1367-2630\/aa54e0"},{"key":"86","doi-asserted-by":"publisher","unstructured":"L. Barbiero, C. Schweizer, M. Aidelsburger, E. Demler, N. Goldman, and F. Grusdt, Science Advances 5 (2019).","DOI":"10.1126\/sciadv.aav7444"},{"key":"87","doi-asserted-by":"publisher","unstructured":"V. Kasper, G. Juzeli\u016bnas, M. Lewenstein, F. Jendrzejewski, and E. Zohar, New Journal of Physics 22, 103027 (2020).","DOI":"10.1088\/1367-2630\/abb961"},{"key":"88","doi-asserted-by":"publisher","unstructured":"C. Senko, P. Richerme, J. Smith, A. Lee, I. Cohen, A. Retzker, and C. Monroe, Phys. Rev. X 5, 021026 (2015).","DOI":"10.1103\/PhysRevX.5.021026"},{"key":"89","doi-asserted-by":"publisher","unstructured":"J. Bender, P. Emonts, E. Zohar, and J. I. Cirac, Phys. Rev. Research 2, 043145 (2020).","DOI":"10.1103\/PhysRevResearch.2.043145"},{"key":"90","doi-asserted-by":"publisher","unstructured":"C. Laflamme, W. Evans, M. Dalmonte, U. Gerber, H. Mej\u00eda-D\u00edaz, et al., Ann. Phys. 370, 117 (2016).","DOI":"10.1016\/j.aop.2016.03.012"},{"key":"91","doi-asserted-by":"publisher","unstructured":"J. Zhang, J. Unmuth-Yockey, J. Zeiher, A. Bazavov, S.-W. Tsai, and Y. Meurice, Phys. Rev. Lett. 121, 223201 (2018).","DOI":"10.1103\/PhysRevLett.121.223201"},{"key":"92","doi-asserted-by":"publisher","unstructured":"Y. Meurice, Phys. Rev. D 102, 014506 (2020).","DOI":"10.1103\/PhysRevD.102.014506"},{"key":"93","doi-asserted-by":"publisher","unstructured":"A. Ammon, T. Hartung, K. Jansen, H. Le\u00f6vey, and J. Volmer, Phys. Rev. D 94, 114508 (2016).","DOI":"10.1103\/PhysRevD.94.114508"},{"key":"94","doi-asserted-by":"publisher","unstructured":"A. Genz, J. Comput. Appl. Math. 157, 187 (2003).","DOI":"10.1016\/S0377-0427(03)00413-8"},{"key":"95","doi-asserted-by":"publisher","unstructured":"A. Alexandru, P. F. Bedaque, S. Harmalkar, H. Lamm, S. Lawrence, and N. C. Warrington (NuQS Collaboration), Phys. Rev. D 100, 114501 (2019).","DOI":"10.1103\/PhysRevD.100.114501"},{"key":"96","doi-asserted-by":"publisher","unstructured":"H. Lamm, S. Lawrence, and Y. Yamauchi (NuQS Collaboration), Phys. Rev. Research 2, 013272 (2020).","DOI":"10.1103\/PhysRevResearch.2.013272"},{"key":"97","doi-asserted-by":"publisher","unstructured":"R. M. Gray, Found. Trends Commun. Inf. Theory 2, 155 (2006).","DOI":"10.1561\/0100000006"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2021-02-04-393\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2021,7,5]],"date-time":"2021-07-05T21:20:42Z","timestamp":1625520042000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2021-02-04-393\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,4]]},"references-count":98,"URL":"https:\/\/doi.org\/10.22331\/q-2021-02-04-393","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,4]]},"article-number":"393"}}