Variational Monte Carlo and the Quantum Enhanced Metropolis-Hastings Algorithm

Variational Monte Carlo and the Quantum Enhanced Metropolis-Hastings Algorithm | 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 Monte Carlo and the Quantum Enhanced Metropolis-Hastings Algorithm Mishka Naicker, Mervlyn Moodley This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7290550/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract This work explores the adaptation of the classical Metropolis-Hastings algorithm into a quantum-enhanced framework to improve sampling efficiency in variational Monte Carlo. Utilizing variational Monte Carlo, and in particular the single thread Monte Carlo method, we estimate the dominant eigenvalue of a symmetric 3 × 3 matrix which could represent the ground state energy of a three-level quantum system. We compare classical and hybrid quantum-classical implementations, where the latter employs the quantum enhanced Metropolis-Hastings algorithm. It is shown that the hybrid version demonstrates accelerated convergence and higher precision in a simulated environment. Quantum Computing Metropolis-Hastings Variational Quantum Monte Carlo Dominant Eigenvalue Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 16 Feb, 2026 Reviews received at journal 30 Jan, 2026 Reviewers agreed at journal 02 Dec, 2025 Reviews received at journal 14 Nov, 2025 Reviewers agreed at journal 30 Sep, 2025 Reviewers agreed at journal 24 Sep, 2025 Reviewers invited by journal 09 Sep, 2025 Editor assigned by journal 07 Aug, 2025 Submission checks completed at journal 05 Aug, 2025 First submitted to journal 04 Aug, 2025 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-7290550","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":497320824,"identity":"7b34e24d-62c0-4fd6-b347-0c9b40a51352","order_by":0,"name":"Mishka Naicker","email":"","orcid":"","institution":"University of KwaZulu-Natal","correspondingAuthor":false,"prefix":"","firstName":"Mishka","middleName":"","lastName":"Naicker","suffix":""},{"id":497320825,"identity":"3771dabc-5ff2-45ea-8dfa-275226853fa9","order_by":1,"name":"Mervlyn Moodley","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3klEQVRIiWNgGAWjYJACiQdAgp+9gZkELQlAQrLnAKlaDG4kEKlFt7354I2EisPRDDffGBv+3MEgz9/A/vADPi1mZ44lWyScOZzbODvHOEHyDIPhjAMMyRJ4tdzIMZNIbDuc2yydY3zAsI2BcQMDwwEitPw7nNsmecb4QGIbg/0GBsbmH4S1NBzO7ZHgMU442MaQuIGBmQ2/LWC/HEvPncGTVmzY2CaRPOMwG5sFXi3HgSH2ocY6d//xw5slf7bZ2Pa3tz++gU8LFDTDGEAnERk9dcQpGwWjYBSMgpEJAOalS9ASkUX6AAAAAElFTkSuQmCC","orcid":"","institution":"University of KwaZulu-Natal","correspondingAuthor":true,"prefix":"","firstName":"Mervlyn","middleName":"","lastName":"Moodley","suffix":""}],"badges":[],"createdAt":"2025-08-04 11:23:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7290550/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7290550/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":88941864,"identity":"184f6303-43e6-4f93-aab3-058573ce7722","added_by":"auto","created_at":"2025-08-13 03:34:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":533988,"visible":true,"origin":"","legend":"","description":"","filename":"Papersub.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7290550/v1_covered_2e3d0542-82f4-47b1-b688-37864bfdd18b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Variational Monte Carlo and the Quantum Enhanced Metropolis-Hastings Algorithm","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"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":"quantum-information-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"qinp","sideBox":"Learn more about [Quantum Information Processing](http://link.springer.com/journal/11128)","snPcode":"11128","submissionUrl":"https://submission.nature.com/new-submission/11128/3","title":"Quantum Information Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Quantum Computing, Metropolis-Hastings, Variational Quantum Monte Carlo, Dominant Eigenvalue","lastPublishedDoi":"10.21203/rs.3.rs-7290550/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7290550/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This work explores the adaptation of the classical Metropolis-Hastings algorithm into a quantum-enhanced framework to improve sampling efficiency in variational Monte Carlo. Utilizing variational Monte Carlo, and in particular the single thread Monte Carlo method, we estimate the dominant eigenvalue of a symmetric 3 × 3 matrix which could represent the ground state energy of a three-level quantum system. We compare classical and hybrid quantum-classical implementations, where the latter employs the quantum enhanced Metropolis-Hastings algorithm. It is shown that the hybrid version demonstrates accelerated convergence and higher precision in a simulated environment.","manuscriptTitle":"Variational Monte Carlo and the Quantum Enhanced Metropolis-Hastings Algorithm","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-13 03:26:47","doi":"10.21203/rs.3.rs-7290550/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-02-16T16:23:29+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-30T19:50:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"186720497399284036247354138110683291847","date":"2025-12-02T09:32:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-14T13:21:16+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"42794556168414657093265329120347886582","date":"2025-09-30T15:15:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"315908496118217733473627324923800271480","date":"2025-09-24T11:31:45+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-09T07:30:38+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-07T18:30:39+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-05T15:58:53+00:00","index":"","fulltext":""},{"type":"submitted","content":"Quantum Information Processing","date":"2025-08-04T11:11:04+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"quantum-information-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"qinp","sideBox":"Learn more about [Quantum Information Processing](http://link.springer.com/journal/11128)","snPcode":"11128","submissionUrl":"https://submission.nature.com/new-submission/11128/3","title":"Quantum Information Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"8f515a28-dfd8-4a98-afe0-75dc73f03650","owner":[],"postedDate":"August 13th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-03-20T15:39:22+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-13 03:26:47","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7290550","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7290550","identity":"rs-7290550","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}