{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T01:37:14Z","timestamp":1775525834271,"version":"3.50.1"},"reference-count":67,"publisher":"IOP Publishing","issue":"2","license":[{"start":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T00:00:00Z","timestamp":1688342400000},"content-version":"vor","delay-in-days":32,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T00:00:00Z","timestamp":1688342400000},"content-version":"tdm","delay-in-days":32,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"National Science Foundation under Cooperative Agreement","award":["PHY-2019786"],"award-info":[{"award-number":["PHY-2019786"]}]},{"name":"NSF CAREER grant","award":["PHY-1848089"],"award-info":[{"award-number":["PHY-1848089"]}]},{"name":"Co-design Center for Quantum Advantage","award":["DE-SC0012704"],"award-info":[{"award-number":["DE-SC0012704"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2023,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We study infinite limits of neural network quantum states (<jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"normal\">\u221e<\/mml:mi>\n                     <\/mml:math>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"mlstace02fieqn1.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula>-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of entanglement entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. The analytic calculations of entanglement entropy bound are tractable because the ensemble statistics are simplified in the Gaussian process limit. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"normal\">\u221e<\/mml:mi>\n                     <\/mml:math>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"mlstace02fieqn2.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula>-NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"normal\">\u221e<\/mml:mi>\n                     <\/mml:math>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"mlstace02fieqn3.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula>-NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"normal\">\u221e<\/mml:mi>\n                     <\/mml:math>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"mlstace02fieqn4.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula>-NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.<\/jats:p>","DOI":"10.1088\/2632-2153\/ace02f","type":"journal-article","created":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T22:49:11Z","timestamp":1687301351000},"page":"025038","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Infinite neural network quantum states: entanglement and training dynamics"],"prefix":"10.1088","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6562-1762","authenticated-orcid":true,"given":"Di","family":"Luo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0535-2622","authenticated-orcid":true,"given":"James","family":"Halverson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2023,7,3]]},"reference":[{"key":"mlstace02fbib1","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1126\/science.aag2302","volume":"355","author":"Carleo","year":"2017","journal-title":"Science"},{"key":"mlstace02fbib2","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/BF02551274","volume":"2","author":"Cybenko","year":"1989","journal-title":"Math. 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Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2022-12-11","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-06-20","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-07-03","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}