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On the base manifold, we use the Mannoury-Fubini-Study metric to find a simple equation relating the Ricci scalar (geometry) and concurrence (entanglement). By calculating the Ricci scalar during a variational quantum eigensolver (VQE) optimization process, this offers us a new perspective to how and why Quantum Natural Gradient outperforms the standard gradient descent. We argue that the key to the Quantum Natural Gradient&amp;apos;s superior performance is its ability to find regions of high negative curvature early in the optimization process. These regions of high negative curvature appear to be important in accelerating the optimization process.<\/jats:p>","DOI":"10.22331\/q-2022-08-23-782","type":"journal-article","created":{"date-parts":[[2022,8,23]],"date-time":"2022-08-23T12:37:58Z","timestamp":1661258278000},"page":"782","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":13,"title":["Connecting geometry and performance of two-qubit parameterized quantum circuits"],"prefix":"10.22331","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0078-5202","authenticated-orcid":false,"given":"Amara","family":"Katabarwa","sequence":"first","affiliation":[{"name":"Zapata Computing, Inc., 100 Federal Street, 20th Floor, Boston, Massachusetts 02110, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sukin","family":"Sim","sequence":"additional","affiliation":[{"name":"Zapata Computing, Inc., 100 Federal Street, 20th Floor, Boston, Massachusetts 02110, USA"},{"name":"Harvard University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8968-591X","authenticated-orcid":false,"given":"Dax Enshan","family":"Koh","sequence":"additional","affiliation":[{"name":"Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pierre-Luc","family":"Dallaire-Demers","sequence":"additional","affiliation":[{"name":"Zapata Computing, Inc., 100 Federal Street, 20th Floor, Boston, Massachusetts 02110, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,8,23]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Marco Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, et al. 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