Variational Quantum Eigensolver: A Comparative Analysis of Classical and Quantum Optimization Methods

Variational Quantum Eigensolver: A Comparative Analysis of Classical and Quantum Optimization Methods | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Variational Quantum Eigensolver: A Comparative Analysis of Classical and Quantum Optimization Methods Duc-Truyen Le, Vu-Linh Nguyen, Ha C. Nguyen, Hung Q. Nguyen, Van-Duy Nguyen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6497487/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this study, we study the Variational Quantum Eigensolver (VQE) application for the Ising model as a test bed model, in which we pivotally delved into several optimization methods, both classical and quantum, and analyzed the quantum advantage that each of these methods offered, and then we proposed a new combinatorial optimization scheme, deemed as QN-SPSA+PSR which combines calculating approximately Fubini-study metric (QN-SPSA) and the exact evaluation of gradient by Parameter-Shift Rule (PSR). The QN-SPSA+PSR method integrates the QN-SPSA computational efficiency with the precise gradient computation of the PSR, improving both stability and convergence speed while maintaining low computational consumption. Our results provide a new potential quantum supremacy in the VQAs's optimization subroutine, even in Quantum Machine Learning's optimization section, and enhance viable paths toward efficient quantum simulations on Noisy Intermediate-Scale Quantum Computing (NISQ) devices. Additionally, we also conducted a detailed study of quantum circuit ansatz structures in order to find the one that would work best with the Ising model and NISQ, in which we utilized the properties of the investigated model. Ising Model Variational Quantum Algorithm Quantum Optimization Ansazt Construction Gradient Estimation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6497487","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":452131491,"identity":"761f5557-fb72-42b0-8204-c6ae86489d43","order_by":0,"name":"Duc-Truyen Le","email":"data:image/png;base64,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","orcid":"","institution":"National Tsing Hua University","correspondingAuthor":true,"prefix":"","firstName":"Duc-Truyen","middleName":"","lastName":"Le","suffix":""},{"id":452131492,"identity":"51abba32-ec6c-4953-a82d-fe3e46f55489","order_by":1,"name":"Vu-Linh Nguyen","email":"","orcid":"","institution":"Ho Chi Minh City University of Science","correspondingAuthor":false,"prefix":"","firstName":"Vu-Linh","middleName":"","lastName":"Nguyen","suffix":""},{"id":452131493,"identity":"fc7b0ceb-f813-4db4-9c35-f804187dbfaa","order_by":2,"name":"Ha C. Nguyen","email":"","orcid":"","institution":"Université PSL","correspondingAuthor":false,"prefix":"","firstName":"Ha","middleName":"C.","lastName":"Nguyen","suffix":""},{"id":452131494,"identity":"6724ff42-760c-4e32-b03e-38731fce5b3a","order_by":3,"name":"Hung Q. Nguyen","email":"","orcid":"","institution":"University of Science, Vietnam National University","correspondingAuthor":false,"prefix":"","firstName":"Hung","middleName":"Q.","lastName":"Nguyen","suffix":""},{"id":452131495,"identity":"9aa2a118-2f87-4122-aceb-01b22c17d533","order_by":4,"name":"Van-Duy Nguyen","email":"","orcid":"","institution":"Phenikaa University","correspondingAuthor":false,"prefix":"","firstName":"Van-Duy","middleName":"","lastName":"Nguyen","suffix":""}],"badges":[],"createdAt":"2025-04-21 15:53:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6497487/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6497487/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":84210466,"identity":"ec1a8b87-c150-4477-a53d-367a774d5383","added_by":"auto","created_at":"2025-06-09 09:53:58","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1464025,"visible":true,"origin":"","legend":"","description":"","filename":"ManusciptVQEEPJQuantum.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6497487/v1_covered_fa489a10-5f09-42cc-a586-6607c43c3ca9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Variational Quantum Eigensolver: A Comparative Analysis of Classical and Quantum Optimization Methods","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Ising Model, Variational Quantum Algorithm, Quantum Optimization, Ansazt Construction, Gradient Estimation","lastPublishedDoi":"10.21203/rs.3.rs-6497487/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6497487/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, we study the Variational Quantum Eigensolver (VQE) application for the Ising model as a test bed model, in which we pivotally delved into several optimization methods, both classical and quantum, and analyzed the quantum advantage that each of these methods offered, and then we proposed a new combinatorial optimization scheme, deemed as QN-SPSA+PSR which combines calculating approximately Fubini-study metric (QN-SPSA) and the exact evaluation of gradient by Parameter-Shift Rule (PSR). The QN-SPSA+PSR method integrates the QN-SPSA computational efficiency with the precise gradient computation of the PSR, improving both stability and convergence speed while maintaining low computational consumption. Our results provide a new potential quantum supremacy in the VQAs's optimization subroutine, even in Quantum Machine Learning's optimization section, and enhance viable paths toward efficient quantum simulations on Noisy Intermediate-Scale Quantum Computing (NISQ) devices. Additionally, we also conducted a detailed study of quantum circuit ansatz structures in order to find the one that would work best with the Ising model and NISQ, in which we utilized the properties of the investigated model.\u003c/p\u003e","manuscriptTitle":"Variational Quantum Eigensolver: A Comparative Analysis of Classical and Quantum Optimization Methods","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-06 05:03:58","doi":"10.21203/rs.3.rs-6497487/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"546edb41-1b1b-47de-8de2-73bdcef38705","owner":[],"postedDate":"May 6th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-06-09T09:53:20+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-06 05:03:58","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6497487","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6497487","identity":"rs-6497487","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}