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To successfully implement such algorithms, one must design efficient quantum circuits that sufficiently approximate the solution space while maintaining a low parameter count and circuit depth. In this paper, develop a method to analyze the dimensional expressivity of parametric quantum circuits. Our technique allows for identifying superfluous parameters in the circuit layout and for obtaining a maximally expressive ansatz with a minimum number of parameters. Using a hybrid quantum-classical approach, we show how to efficiently implement the expressivity analysis using quantum hardware, and we provide a proof of principle demonstration of this procedure on IBM's quantum hardware. We also discuss the effect of symmetries and demonstrate how to incorporate or remove symmetries from the parametrized ansatz.<\/jats:p>","DOI":"10.22331\/q-2021-03-29-422","type":"journal-article","created":{"date-parts":[[2021,3,29]],"date-time":"2021-03-29T15:10:00Z","timestamp":1617030600000},"page":"422","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":54,"title":["Dimensional Expressivity Analysis of Parametric Quantum Circuits"],"prefix":"10.22331","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5022-9506","authenticated-orcid":false,"given":"Lena","family":"Funcke","sequence":"first","affiliation":[{"name":"Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6133-5232","authenticated-orcid":false,"given":"Tobias","family":"Hartung","sequence":"additional","affiliation":[{"name":"Computation-Based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Street, 2121 Nicosia, Cyprus"},{"name":"Department of Mathematics, King\u2019s College London, Strand, London WC2R 2LS, United Kingdom"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1574-7591","authenticated-orcid":false,"given":"Karl","family":"Jansen","sequence":"additional","affiliation":[{"name":"NIC, DESY Zeuthen, Platanenallee 6, 15738 Zeuthen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7693-350X","authenticated-orcid":false,"given":"Stefan","family":"K\u00fchn","sequence":"additional","affiliation":[{"name":"Computation-Based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Street, 2121 Nicosia, Cyprus"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4708-9340","authenticated-orcid":false,"given":"Paolo","family":"Stornati","sequence":"additional","affiliation":[{"name":"NIC, DESY Zeuthen, Platanenallee 6, 15738 Zeuthen, Germany"},{"name":"Institut f\u00fcr Physik, Humboldt-Universit\u00e4t zu Berlin, Zum Gro\u00dfen Windkanal 6, D-12489 Berlin, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2021,3,29]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"J. 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