{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:53:18Z","timestamp":1760143998695,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T00:00:00Z","timestamp":1710288000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000015","name":"National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-AC02-05CH11231","NERSC DDR-ERCAP0025759","DE-SC0012447","DE-SC0022148","DE-SC0024407"],"award-info":[{"award-number":["DE-AC02-05CH11231","NERSC DDR-ERCAP0025759","DE-SC0012447","DE-SC0022148","DE-SC0024407"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NERSC award","award":["DE-AC02-05CH11231","NERSC DDR-ERCAP0025759","DE-SC0012447","DE-SC0022148","DE-SC0024407"],"award-info":[{"award-number":["DE-AC02-05CH11231","NERSC DDR-ERCAP0025759","DE-SC0012447","DE-SC0022148","DE-SC0024407"]}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy (DOE)","doi-asserted-by":"publisher","award":["DE-AC02-05CH11231","NERSC DDR-ERCAP0025759","DE-SC0012447","DE-SC0022148","DE-SC0024407"],"award-info":[{"award-number":["DE-AC02-05CH11231","NERSC DDR-ERCAP0025759","DE-SC0012447","DE-SC0022148","DE-SC0024407"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"name":"College of Liberal Arts and Sciences Research Fund at the University of Kansas","award":["DE-AC02-05CH11231","NERSC DDR-ERCAP0025759","DE-SC0012447","DE-SC0022148","DE-SC0024407"],"award-info":[{"award-number":["DE-AC02-05CH11231","NERSC DDR-ERCAP0025759","DE-SC0012447","DE-SC0022148","DE-SC0024407"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper presents a comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNNs) and Quantum Neural Networks (QNNs), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENNs) and Deep Neural Networks (DNNs). We evaluate the performance of each network with three two-dimensional toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training dataset. Our results show that the Z2\u00d7Z2 EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.<\/jats:p>","DOI":"10.3390\/axioms13030188","type":"journal-article","created":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T03:46:31Z","timestamp":1710301591000},"page":"188","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["\u21242 \u00d7 \u21242 Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networks"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1000-3454","authenticated-orcid":false,"given":"Zhongtian","family":"Dong","sequence":"first","affiliation":[{"name":"Department of Physics & Astronomy, University of Kansas, Lawrence, KS 66045, USA"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-2626-3752","authenticated-orcid":false,"given":"Mar\u00e7al","family":"Comajoan Cara","sequence":"additional","affiliation":[{"name":"Department of Signal Theory and Communications, Polytechnic University of Catalonia, 08034 Barcelona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-8116-1950","authenticated-orcid":false,"given":"Gopal Ramesh","family":"Dahale","sequence":"additional","affiliation":[{"name":"Indian Institute of Technology Bhilai, Kutelabhata, Khapri, District-Durg, Chhattisgarh 491001, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0355-2076","authenticated-orcid":false,"given":"Roy T.","family":"Forestano","sequence":"additional","affiliation":[{"name":"Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6222-8102","authenticated-orcid":false,"given":"Sergei","family":"Gleyzer","sequence":"additional","affiliation":[{"name":"Department of Physics & Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5450-2207","authenticated-orcid":false,"given":"Daniel","family":"Justice","sequence":"additional","affiliation":[{"name":"Software Engineering Institute, Carnegie Mellon University, 4500 Fifth Avenue, Pittsburgh, PA 15213, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4515-7303","authenticated-orcid":false,"given":"Kyoungchul","family":"Kong","sequence":"additional","affiliation":[{"name":"Department of Physics & Astronomy, University of Kansas, Lawrence, KS 66045, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3890-0066","authenticated-orcid":false,"given":"Tom","family":"Magorsch","sequence":"additional","affiliation":[{"name":"Physik-Department, Technische Universit\u00e4t M\u00fcnchen, James-Franck-Str. 1, 85748 Garching, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4182-9096","authenticated-orcid":false,"given":"Konstantin T.","family":"Matchev","sequence":"additional","affiliation":[{"name":"Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3074-998X","authenticated-orcid":false,"given":"Katia","family":"Matcheva","sequence":"additional","affiliation":[{"name":"Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6683-6463","authenticated-orcid":false,"given":"Eyup B.","family":"Unlu","sequence":"additional","affiliation":[{"name":"Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,13]]},"reference":[{"key":"ref_1","unstructured":"Shanahan, P., Terao, K., and Whiteson, D. 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