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In this work we demonstrate that purely classical resources can be used to optimize quantum circuits in an approximate but robust manner such that we can bridge the resources that we have from high performance computing and see a direct transition to quantum advantage. We show this through the sparse wave function circuit solvers, which we detail here, and demonstrate a region of efficient classic simulation. With such tools, we can avoid the many problems that plague circuit optimization for circuits with hundreds of qubits using only practical and reasonable classical computing resources. These tools allow us to probe the true benefit of variational optimization approaches on quantum computers, thus opening the window to what can be expected with near term hardware for physical systems. We demonstrate this with a unitary coupled cluster ansatz on various molecules up to 64 qubits with tens of thousands of variational parameters.<\/jats:p>","DOI":"10.1063\/5.0251601","type":"journal-article","created":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T05:43:34Z","timestamp":1740116614000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":10,"title":["Large-scale sparse wave function circuit simulator for applications with the variational quantum eigensolver"],"prefix":"10.1063","volume":"162","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9402-9442","authenticated-orcid":false,"given":"J. Wayne","family":"Mullinax","sequence":"first","affiliation":[{"name":"KBR, Inc., Intelligent Systems Division, NASA Ames Research Center 1 , Moffet Field, California 94035,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9577-8485","authenticated-orcid":false,"given":"Norm M.","family":"Tubman","sequence":"additional","affiliation":[{"name":"NASA Ames Research Center 2 , Moffett Field, California 94035,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2025,2,21]]},"reference":[{"key":"2025022110424908700_c1","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1038\/s41534-019-0217-0","article-title":"Simulating quantum many-body dynamics on a current digital quantum computer","volume":"5","year":"2019","journal-title":"npj Quantum Inf."},{"key":"2025022110424908700_c2","doi-asserted-by":"publisher","first-page":"12685","DOI":"10.1021\/acs.chemrev.9b00829","article-title":"Quantum algorithms for quantum chemistry and quantum materials science","volume":"120","year":"2020","journal-title":"Chem. 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