Hybrid classical-quantum computation of heat diffusion in multilayer materials

Hybrid classical-quantum computation of heat diffusion in multilayer materials | 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 Hybrid classical-quantum computation of heat diffusion in multilayer materials Sasan Moradi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6887498/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 Solving the 1D time-dependent heat diffusion equation using the Finite Difference Time Domain method is simplified to multiplying a tridiagonal sparse matrix by a vector representing the heat (temperature) distribution. To implement this multiplication operation with a quantum algorithm, we design and describe a quantum circuit for matrix-vector multiplication. The sparse matrix is loaded using recursive divide-and-conquer approach with binary tree preorder traversal. Subsequently, heat diffusion is simulated for a two-layer medium with different diffusion coefficients, and its distribution across the layers is tracked over time. The critical time is approximated based on the distribution of diffused heat. The critical time from the numerical simulation was validated using two empirical methods. It matches well with the more complex method, while the simpler method yielded a different value. Quantum Computing heat equation matrix-vector multiplication classical divide-and-conquer Full Text Additional Declarations No competing interests reported. Supplementary Files Supplement.pdf 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-6887498","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":471864854,"identity":"ffaccc56-09f5-4d92-b300-9537b066b37b","order_by":0,"name":"Sasan Moradi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7ElEQVRIiWNgGAWjYLADiYQKIMnM3ECKljMgLYykaGFsA1EEtMi3H3/84ecOhmh+6cMPbzycVxvN3w7U8qNiG04tBmdyzCR7zzDkzuxLM7ZI3HY8d8ZhxgbGnjO3cWthyGFj4G1jyN1whsFMInHbsdwGoBZmxjbcWuT7nz/++Beshf2bROKcY7nzCWlhuJFgIA2xhQdoS0NN7gZCWgxuvDGTlm2TyJ3Zw1NskXDsQO5GoJaD+Pwi35/++OPbNpvcfh72jTd/1NTlzjt/+OCDHxV4HAYBEjDGYTB5gJB6ZFBHiuJRMApGwSgYIQAAIJdbvCtA3TwAAAAASUVORK5CYII=","orcid":"","institution":"Medical university of Vienna","correspondingAuthor":true,"prefix":"","firstName":"Sasan","middleName":"","lastName":"Moradi","suffix":""}],"badges":[],"createdAt":"2025-06-13 10:53:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6887498/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6887498/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86221506,"identity":"8fa59456-a790-4c92-8fb6-8aee5d8d639a","added_by":"auto","created_at":"2025-07-08 07:09:14","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":467115,"visible":true,"origin":"","legend":"","description":"","filename":"tpvnmxxkzhrnhdsrbbkfxhchzkcxkjhy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6887498/v1_covered_855d4366-cb6b-47c2-8b07-b770c2bdfd8f.pdf"},{"id":85311145,"identity":"1c8f67b4-8daa-41aa-ab12-4bba931acd41","added_by":"auto","created_at":"2025-06-24 13:39:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":273969,"visible":true,"origin":"","legend":"","description":"","filename":"Supplement.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6887498/v1/241bfc5cd66be93847009e40.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Hybrid classical-quantum computation of heat diffusion in multilayer materials","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 Computing, heat equation, matrix-vector multiplication, classical divide-and-conquer","lastPublishedDoi":"10.21203/rs.3.rs-6887498/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6887498/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSolving the 1D time-dependent heat diffusion equation using the Finite Difference Time Domain method is simplified to multiplying a tridiagonal sparse matrix by a vector representing the heat (temperature) distribution. 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