{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T04:47:24Z","timestamp":1781326044686,"version":"3.54.1"},"reference-count":87,"publisher":"IOP Publishing","issue":"4","license":[{"start":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T00:00:00Z","timestamp":1672185600000},"content-version":"vor","delay-in-days":27,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T00:00:00Z","timestamp":1672185600000},"content-version":"tdm","delay-in-days":27,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"NSF","award":["1125565"],"award-info":[{"award-number":["1125565"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2022,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Rapid developments of quantum information technology show promising opportunities for simulating quantum field theory in near-term quantum devices. In this work, we formulate the theory of (time-dependent) variational quantum simulation of the <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mn>1<\/mml:mn>\n                        <mml:mo>+<\/mml:mo>\n                        <mml:mn>1<\/mml:mn>\n                     <\/mml:math>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"mlstaca06bieqn1.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula> dimensional <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi>\u03bb<\/mml:mi>\n                        <mml:msup>\n                           <mml:mi>\u03d5<\/mml:mi>\n                           <mml:mn>4<\/mml:mn>\n                        <\/mml:msup>\n                     <\/mml:math>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"mlstaca06bieqn2.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula> quantum field theory including encoding, state preparation, and time evolution, with several numerical simulation results. These algorithms could be understood as near-term variational quantum circuit (quantum neural network) analogs of the Jordan\u2013Lee\u2013Preskill algorithm, the basic algorithm for simulating quantum field theory using universal quantum devices. Besides, we highlight the advantages of encoding with harmonic oscillator basis based on the Lehmann\u2014Symanzik\u2014Zimmermann reduction formula and several computational efficiency such as when implementing a bosonic version of the unitary coupled cluster ansatz to prepare initial states. We also discuss how to circumvent the \u2018spectral crowding\u2019 problem in the quantum field theory simulation and appraise our algorithm by both state and subspace fidelities.<\/jats:p>","DOI":"10.1088\/2632-2153\/aca06b","type":"journal-article","created":{"date-parts":[[2022,11,4]],"date-time":"2022-11-04T22:25:46Z","timestamp":1667600746000},"page":"045030","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":16,"title":["Towards a variational Jordan\u2013Lee\u2013Preskill quantum algorithm"],"prefix":"10.1088","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1669-8039","authenticated-orcid":true,"given":"Junyu","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1473-6492","authenticated-orcid":true,"given":"Zimu","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Han","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiao","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinzhao","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2022,12,28]]},"reference":[{"key":"mlstaca06bbib1","doi-asserted-by":"publisher","first-page":"79","DOI":"10.22331\/q-2018-08-06-79","volume":"2","author":"Preskill","year":"2018","journal-title":"Quantum"},{"key":"mlstaca06bbib2","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1038\/s41586-019-1666-5","volume":"574","author":"Arute","year":"2019","journal-title":"Nature"},{"key":"mlstaca06bbib3","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1007\/BF02650179","volume":"21","author":"Feynman","year":"1982","journal-title":"Int. J. Theor. Phys."},{"key":"mlstaca06bbib4","doi-asserted-by":"publisher","first-page":"024","DOI":"10.22323\/1.334.0024","volume":"334","author":"Preskill","year":"2018","journal-title":"Proc. Sci."},{"key":"mlstaca06bbib5","article-title":"Does Richard Feynman dream of electric sheep? Topics on quantum field theory, quantum computing, and computer science","author":"Liu","year":"2021"},{"key":"mlstaca06bbib6","doi-asserted-by":"publisher","first-page":"1130","DOI":"10.1126\/science.1217069","volume":"336","author":"Jordan","year":"2012","journal-title":"Science"},{"key":"mlstaca06bbib7","doi-asserted-by":"publisher","first-page":"1014","DOI":"10.5555\/2685155.2685163","volume":"14","author":"Jordan","year":"2014","journal-title":"Quantum Inf. Comput."},{"key":"mlstaca06bbib8","author":"Milsted","year":"2020"},{"key":"mlstaca06bbib9","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms5213","volume":"5","author":"Peruzzo","year":"2014","journal-title":"Nat. Commun."},{"key":"mlstaca06bbib10","author":"Farhi","year":"2014"},{"key":"mlstaca06bbib11","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/18\/2\/023023","volume":"18","author":"McClean","year":"2016","journal-title":"New J. Phys."},{"key":"mlstaca06bbib12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.7.021050","volume":"7","author":"Li","year":"2017","journal-title":"Phys. Rev. X"},{"key":"mlstaca06bbib13","doi-asserted-by":"publisher","first-page":"191","DOI":"10.22331\/q-2019-10-07-191","volume":"3","author":"Yuan","year":"2019","journal-title":"Quantum"},{"key":"mlstaca06bbib14","doi-asserted-by":"publisher","DOI":"10.7566\/JPSJ.90.032001","volume":"90","author":"Endo","year":"2021","journal-title":"J. Phys. Soc. Japan"},{"key":"mlstaca06bbib15","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1038\/s42254-021-00348-9","volume":"3","author":"Cerezo","year":"2021","journal-title":"Nat. Rev. Phys."},{"key":"mlstaca06bbib16","author":"Zhang","year":"2020"},{"key":"mlstaca06bbib17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.125.010501","volume":"125","author":"Endo","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"mlstaca06bbib18","doi-asserted-by":"publisher","first-page":"2181","DOI":"10.1016\/j.scib.2021.06.023","volume":"66","author":"Xu","year":"2021","journal-title":"Sci. Bull."},{"key":"mlstaca06bbib19","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1038\/s41534-019-0187-2","volume":"5","author":"McArdle","year":"2019","journal-title":"npj Quantum Inf."},{"key":"mlstaca06bbib20","author":"Childs","year":"2019"},{"key":"mlstaca06bbib21","author":"Low","year":"2016"},{"key":"mlstaca06bbib22","doi-asserted-by":"publisher","first-page":"306","DOI":"10.22331\/q-2020-08-10-306","volume":"4","author":"Shaw","year":"2020","journal-title":"Quantum"},{"key":"mlstaca06bbib23","article-title":"Digital quantum simulation of the schwinger model with topological term via adiabatic state preparation","author":"Chakraborty","year":"2020"},{"key":"mlstaca06bbib24","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/aadb71","volume":"20","author":"Bender","year":"2018","journal-title":"New J. Phys."},{"key":"mlstaca06bbib25","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1038\/s41586-019-1177-4","volume":"569","author":"Kokail","year":"2019","journal-title":"Nature"},{"key":"mlstaca06bbib26","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.2.030334","volume":"2","author":"Paulson","year":"2021","journal-title":"PRX Quantum"},{"key":"mlstaca06bbib27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41534-020-0278-0","volume":"6","author":"Sawaya","year":"2020","journal-title":"npj Quantum Inf."},{"key":"mlstaca06bbib28","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/978-3-319-00627-7_90","volume":"25","author":"Kallen","year":"1952","journal-title":"Helv. Phys. Acta"},{"key":"mlstaca06bbib29","doi-asserted-by":"publisher","first-page":"342","DOI":"10.1007\/BF02783624","volume":"11","author":"Lehmann","year":"1954","journal-title":"Nuovo Cimento"},{"key":"mlstaca06bbib30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.99.052335","volume":"99","author":"Klco","year":"2019","journal-title":"Phys. Rev. A"},{"key":"mlstaca06bbib31","author":"Robert","year":"2019"},{"key":"mlstaca06bbib32","author":"Kitaev","year":"2008"},{"key":"mlstaca06bbib33","article-title":"The Hamiltonian with truncated energy levels is represented in a low-energy subspace"},{"key":"mlstaca06bbib34","author":"Liu","year":"2022"},{"key":"mlstaca06bbib35","author":"Liu","year":"2021"},{"key":"mlstaca06bbib36","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.6.021011","volume":"6","author":"O\u2019Malley","year":"2016","journal-title":"Phys. Rev. X"},{"key":"mlstaca06bbib37","doi-asserted-by":"publisher","DOI":"10.1103\/physreva.95.020501","volume":"95","author":"Shen","year":"2017","journal-title":"Phys. Rev. A"},{"key":"mlstaca06bbib38","doi-asserted-by":"publisher","first-page":"5725","DOI":"10.1039\/C9SC01313J","volume":"10","author":"McArdle","year":"2019","journal-title":"Chem. Sci."},{"key":"mlstaca06bbib39","doi-asserted-by":"publisher","first-page":"6842","DOI":"10.1039\/D0SC01908A","volume":"11","author":"Ollitrault","year":"2020","journal-title":"Chem. Sci."},{"key":"mlstaca06bbib40","doi-asserted-by":"publisher","first-page":"269","DOI":"10.22331\/q-2020-05-25-269","volume":"4","author":"Stokes","year":"2020","journal-title":"Quantum"},{"key":"mlstaca06bbib41","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1038\/s41567-019-0704-4","volume":"16","author":"Motta","year":"2020","journal-title":"Nat. Phys."},{"key":"mlstaca06bbib42","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.100.022332","volume":"100","author":"Landsman","year":"2019","journal-title":"Phys. Rev. A"},{"key":"mlstaca06bbib43","article-title":"However, for this set of parameter choices, the energies of two-particle and three-particle zero-momentum states are lower than the single-particle excited states"},{"key":"mlstaca06bbib44","doi-asserted-by":"publisher","first-page":"7","DOI":"10.21468\/SciPostPhysLectNotes.7","author":"Vanderstraeten","year":"2019","journal-title":"SciPost Phys. Lect. Notes"},{"key":"mlstaca06bbib45","article-title":"There are some recent research about quantum simulation in the low energy subspace, see [81]"},{"key":"mlstaca06bbib46","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.127.040501","volume":"127","author":"Yuan","year":"2021","journal-title":"Phys. Rev. Lett."},{"key":"mlstaca06bbib47","author":"Sun","year":"2021"},{"key":"mlstaca06bbib48","article-title":"For sufficiently small \u03bb 0, the eigenstates in the free theory is close to that in the interacting theory"},{"key":"mlstaca06bbib49","article-title":"Discretizing quantum field theories for quantum simulation","author":"Farrelly","year":"2020"},{"key":"mlstaca06bbib50","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.100.034518","volume":"100","author":"Lamm","year":"2019","journal-title":"Phys. Rev. D"},{"key":"mlstaca06bbib51","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.3.041018","volume":"3","author":"Hauke","year":"2013","journal-title":"Phys. Rev. X"},{"key":"mlstaca06bbib52","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.10.021041","volume":"10","author":"Surace","year":"2020","journal-title":"Phys. Rev. X"},{"key":"mlstaca06bbib53","author":"Alexeev","year":"2020"},{"key":"mlstaca06bbib54","author":"von Burg","year":"2020"},{"key":"mlstaca06bbib55","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.95.042308","volume":"95","author":"McClean","year":"2017","journal-title":"Phys. Rev. A"},{"key":"mlstaca06bbib56","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.7.021050","volume":"7","author":"Li","year":"2017","journal-title":"Phys. Rev. X"},{"key":"mlstaca06bbib57","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.98.062339","volume":"98","author":"Bonet-Monroig","year":"2018","journal-title":"Phys. Rev. A"},{"key":"mlstaca06bbib58","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.119.180509","volume":"119","author":"Temme","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"mlstaca06bbib59","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.8.031027","volume":"8","author":"Endo","year":"2018","journal-title":"Phys. Rev. X"},{"key":"mlstaca06bbib60","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.8.011021","volume":"8","author":"Colless","year":"2018","journal-title":"Phys. Rev. X"},{"key":"mlstaca06bbib61","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.99.012338","volume":"99","author":"Otten","year":"2019","journal-title":"Phys. Rev. A"},{"key":"mlstaca06bbib62","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.99.012334","volume":"99","author":"Endo","year":"2019","journal-title":"Phys. Rev. A"},{"key":"mlstaca06bbib63","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.180501","volume":"122","author":"McArdle","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"mlstaca06bbib64","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevApplied.15.034026","volume":"15","author":"Sun","year":"2021","journal-title":"Phys. Rev. Appl."},{"key":"mlstaca06bbib65","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1038\/s41586-019-1040-7","volume":"567","author":"Kandala","year":"2019","journal-title":"Nature"},{"key":"mlstaca06bbib66","doi-asserted-by":"publisher","first-page":"1084","DOI":"10.1126\/science.abb9811","volume":"369","author":"Quantum","year":"2020","journal-title":"Science"},{"key":"mlstaca06bbib67","article-title":"Scalable error mitigation for noisy quantum circuits produces competitive expectation values","author":"Kim","year":"2021"},{"key":"mlstaca06bbib68","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1038\/nature23879","volume":"549","author":"Kandala","year":"2017","journal-title":"Nature"},{"key":"mlstaca06bbib69","author":"Wu","year":"2021"},{"key":"mlstaca06bbib70","doi-asserted-by":"publisher","DOI":"10.1063\/1.5141458","volume":"152","author":"Verteletskyi","year":"2020","journal-title":"J. Chem. Phys."},{"key":"mlstaca06bbib71","author":"Hadfield","year":"2020"},{"key":"mlstaca06bbib72","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.022060","volume":"2","author":"Torlai","year":"2020","journal-title":"Phys. Rev. Res."},{"key":"mlstaca06bbib73","doi-asserted-by":"publisher","first-page":"1050","DOI":"10.1038\/s41567-020-0932-7","volume":"16","author":"Huang","year":"2020","journal-title":"Nat. Phys."},{"key":"mlstaca06bbib74","author":"Huang","year":"2021"},{"key":"mlstaca06bbib75","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.100401","volume":"124","author":"Cotler","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"mlstaca06bbib76","author":"Hadfield","year":"2021"},{"key":"mlstaca06bbib77","author":"Hillmich","year":"2021"},{"key":"mlstaca06bbib78","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.127.200501","article-title":"Experimental quantum state measurement with classical shadows","author":"Zhang","year":"2021"},{"key":"mlstaca06bbib79","author":"Macridin","year":"2021"},{"key":"mlstaca06bbib80","author":"Kurkcuoglu","year":"2021"},{"key":"mlstaca06bbib81","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41534-021-00451-w","volume":"7","author":"\u015eahino\u011flu","year":"2021","journal-title":"npj Quantum Inf."},{"key":"mlstaca06bbib82"},{"key":"mlstaca06bbib83","doi-asserted-by":"publisher","first-page":"912","DOI":"10.1119\/1.17013","volume":"60","author":"Diamond","year":"1992","journal-title":"Am. J. Phys."},{"key":"mlstaca06bbib84","doi-asserted-by":"publisher","first-page":"981","DOI":"10.1090\/S0002-9939-1961-0132852-2","volume":"12","author":"Indritz","year":"1961","journal-title":"Proc. Am. Math. Soc."},{"key":"mlstaca06bbib85","author":"Shirai","year":"2021"},{"key":"mlstaca06bbib86","author":"Altland","year":"2010"},{"key":"mlstaca06bbib87"}],"container-title":["Machine Learning: Science and Technology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/aca06b","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/aca06b\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/aca06b","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/aca06b\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/aca06b\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/aca06b\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/aca06b\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/aca06b\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T10:00:51Z","timestamp":1672221651000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/aca06b"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,1]]},"references-count":87,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,12,28]]},"published-print":{"date-parts":[[2022,12,1]]}},"URL":"https:\/\/doi.org\/10.1088\/2632-2153\/aca06b","relation":{},"ISSN":["2632-2153"],"issn-type":[{"value":"2632-2153","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,1]]},"assertion":[{"value":"Towards a variational Jordan\u2013Lee\u2013Preskill quantum algorithm","name":"article_title","label":"Article Title"},{"value":"Machine Learning: Science and Technology","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2022 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2022-08-15","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2022-11-04","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2022-12-28","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}