Machine-Learning-Assisted Parameterization of Quantum Walk Algorithms

Machine-Learning-Assisted Parameterization of Quantum Walk Algorithms | 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Article Machine-Learning-Assisted Parameterization of Quantum Walk Algorithms Parham Ghayour This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8391412/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 Quantum walk algorithms constitute a central primitive in quantum computation, yet their practical performance often depends sensitively on the choice of execution parameters such as walk depth and initial state. Analytical parameter choices are typically conservative and instance-agnostic, which can lead to suboptimal behavior on specific problem instances. In this work, we propose a general framework for machine-learning-assisted parameterization of quantum walk algorithms, in which classical learning is used to adapt algorithmic parameters without modifying the underlying quantum decision logic. The machine learning component op erates exclusively as a classical control layer, preserving correctness guarantees while improving average-case performance. We demonstrate the framework through an application to the s–t connectivity problem, a canonical benchmark in graph algorithms and complexity theory. Classical simulations of discrete-time quantum walks on randomly generated sparse graphs show that ML-assisted pa rameter selection substantially improves success probability compared to fixed-parameter base lines, yielding multiplicative gains in average performance. These improvements are achieved despite only coarse prediction accuracy, highlighting the robustness of the approach. The results suggest a principled role for machine learning as an adaptive optimization layer in quantum algorithms, offering a practical path toward hybrid quantum–classical methods that enhance performance while maintaining theoretical soundness Quantum walks Machine learning Hybrid quantum–classical algorithms s–t connectivity Graph algorithms Quantum algorithms Full Text Additional Declarations The authors declare no competing interests. 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. 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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-8391412","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":562150860,"identity":"33b691ea-9334-4bb3-bac3-85aa7c33b8dc","order_by":0,"name":"Parham Ghayour","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0001-5607-1532","institution":"Sorbonne university","correspondingAuthor":true,"prefix":"","firstName":"Parham","middleName":"","lastName":"Ghayour","suffix":""}],"badges":[],"createdAt":"2025-12-18 05:51:07","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8391412/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8391412/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99309484,"identity":"f241bbf5-8ad2-402f-9476-42aa9b68e1eb","added_by":"auto","created_at":"2025-12-31 16:10:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":275800,"visible":true,"origin":"","legend":"","description":"","filename":"quantumstconnectivity1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8391412/v1_covered_f27927c2-a860-437f-b6f2-0745a2922ba4.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eMachine-Learning-Assisted Parameterization of Quantum Walk Algorithms\u003c/p\u003e","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":" Quantum walks, Machine learning, Hybrid quantum–classical algorithms, s–t connectivity, Graph algorithms, Quantum algorithms","lastPublishedDoi":"10.21203/rs.3.rs-8391412/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8391412/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eQuantum walk algorithms constitute a central primitive in quantum computation, yet their practical performance often depends sensitively on the choice of execution parameters such as walk depth and initial state. 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