PVLS: A Learning-Based Parameter Initialization Method for Variational Quantum Linear Solvers

PVLS: A Learning-Based Parameter Initialization Method for Variational Quantum Linear Solvers | 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 PVLS: A Learning-Based Parameter Initialization Method for Variational Quantum Linear Solvers Youla Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8253544/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 Variational quantum linear solvers (VQLSs) are a promising class of hybrid quantum--classical algorithms for solving linear systems on near-term quantum devices. However, the performance of VQLSs is often impeded by barren plateaus, particularly when using randomly initialized variational quantum circuits (VQCs). To mitigate this issue, we propose \textit{PVLS}, a GNN-based parameter initialization framework that improves both convergence speed and final solution quality. By reformulating the linear system $A\boldsymbol{x} = \boldsymbol{b}$ as a graph with $A$ encoded in the edges and $\boldsymbol{b}$ as node features, PVLS learns to predict effective initial VQC parameters. Our method is trained on thousands of randomly generated matrices with varying dimensions ($n\in[4,10]$), using optimized VQC parameters as ground-truth labels. On unseen test instances, PVLS reduces the initial cost by an average of 81.3% and the final loss by 71% compared to random initialization. PVLS also accelerates convergence, reducing the number of optimization steps by more than 60% on average. We further evaluate PVLS on ten real-world sparse matrices, demonstrating its generalization capability and robustness. Our results highlight the utility of machine-learned priors in improving the trainability of VQLSs and alleviating optimization challenges in variational quantum algorithms. Parameter Prediction Graph Neural Networks Variational Quantum Linear Solvers 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. 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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-8253544","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":567828350,"identity":"8f98d755-19b6-4bba-9cc7-85b1bb47f3dc","order_by":0,"name":"Youla Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtElEQVRIiWNgGAWjYBADGX5mEMVGghYeyWaStRgcIFaLwfGzh1/zVBzmMT7OY8DwoewwEVrO5KVZ85w5zGN2mMeAccY5YrQcyDEz5m2DaGEGMojQcv4NRItxM1DLX6K03MgxfgzSYsAMRIzEaJG88caMcc6ZdB6Jw2wFB3vOpRPWwnc+x/jDmwprOf7+wxsf/CizJqxF4QADmxQPlHOAsHogkG9gYP74gyilo2AUjIJRMGIBAI94OEXwR02uAAAAAElFTkSuQmCC","orcid":"","institution":"Indiana University Bloomington Department of Intelligent Systems Engineering","correspondingAuthor":true,"prefix":"","firstName":"Youla","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2025-12-01 19:38:02","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8253544/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8253544/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102748701,"identity":"fb487430-693f-4570-b308-fdf16a092273","added_by":"auto","created_at":"2026-02-16 09:11:24","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2583465,"visible":true,"origin":"","legend":"","description":"","filename":"PVLSALearningbasedParameterPredictionTechniqueforVariationalQuantumLinearSolvers5.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8253544/v1_covered_269436c3-877e-480e-b76e-5c19778d5207.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"PVLS: A Learning-Based Parameter Initialization Method for Variational Quantum Linear Solvers","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Parameter Prediction, Graph Neural Networks, Variational Quantum Linear Solvers","lastPublishedDoi":"10.21203/rs.3.rs-8253544/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8253544/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Variational quantum linear solvers (VQLSs) are a promising class of hybrid quantum--classical algorithms for solving linear systems on near-term quantum devices. However, the performance of VQLSs is often impeded by barren plateaus, particularly when using randomly initialized variational quantum circuits (VQCs). To mitigate this issue, we propose \\textit{PVLS}, a GNN-based parameter initialization framework that improves both convergence speed and final solution quality. By reformulating the linear system $A\\boldsymbol{x} = \\boldsymbol{b}$ as a graph with $A$ encoded in the edges and $\\boldsymbol{b}$ as node features, PVLS learns to predict effective initial VQC parameters. Our method is trained on thousands of randomly generated matrices with varying dimensions ($n\\in[4,10]$), using optimized VQC parameters as ground-truth labels. On unseen test instances, PVLS reduces the initial cost by an average of 81.3\\% and the final loss by 71\\% compared to random initialization. PVLS also accelerates convergence, reducing the number of optimization steps by more than 60\\% on average. We further evaluate PVLS on ten real-world sparse matrices, demonstrating its generalization capability and robustness. Our results highlight the utility of machine-learned priors in improving the trainability of VQLSs and alleviating optimization challenges in variational quantum algorithms.","manuscriptTitle":"PVLS: A Learning-Based Parameter Initialization Method for Variational Quantum Linear Solvers","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-29 02:40:47","doi":"10.21203/rs.3.rs-8253544/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":"8158c8be-32f2-4d14-af31-3597b98217f7","owner":[],"postedDate":"January 29th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-02-15T04:38:43+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-29 02:40:47","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8253544","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8253544","identity":"rs-8253544","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}