Dimension reduction with structure-aware quantum circuits for hybrid machine learning

Dimension reduction with structure-aware quantum circuits for hybrid machine learning | 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 Dimension reduction with structure-aware quantum circuits for hybrid machine learning Ammar Daskin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7264732/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 Schmidt decomposition of a vector can be understood as writing the singular value decomposition (SVD) in vector form. A vector can be written as a linear combination of tensor product of two dimensional vectors by recursively applying Schmidt decompositions via SVD to all subsystems. Given a vector expressed as a linear combination of tensor products, using only the k principal terms yields a k-rank approximation of the vector. Therefore, writing a vector in this reduced form allows to retain most important parts of the vector while removing small noises from it, analogous to SVD-based denoising. In this paper, we show that quantum circuits designed based on a value k (determined from the tensor network decomposition of the mean vector of the training sample) can approximate the reduced-form representations of entire datasets. We then employ this circuit ansatz with a classical neural network head to construct a hybrid machine learning model. Since the output of the quantum circuit for an 2n dimensional vector is an n dimensional probability vector, this provides an exponential compression of the input and potentially can reduce the number of learnable parameters for training large-scale models. We use datasets provided in the Python scikit-learn module for the experiments. The results confirm the quantum circuit is able to compress data successfully to provide effective k-rank approximations to the classical processing component. Quantum dimension reduction quantum machine learning Schmidt decomposition quantum circuits 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. 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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-7264732","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":503171475,"identity":"8481f55d-f598-4695-8577-cb0a3834adae","order_by":0,"name":"Ammar Daskin","email":"data:image/png;base64,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","orcid":"","institution":"Istanbul Medeniyet University","correspondingAuthor":true,"prefix":"","firstName":"Ammar","middleName":"","lastName":"Daskin","suffix":""}],"badges":[],"createdAt":"2025-07-31 17:38:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7264732/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7264732/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96243824,"identity":"e3631052-48b6-4752-8181-5c3a20e03d12","added_by":"auto","created_at":"2025-11-19 07:17:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2857228,"visible":true,"origin":"","legend":"","description":"","filename":"ghzqvsswcjypypvcztybhtctdxpggfcp.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7264732/v1_covered_8fb4d7c1-af13-42c8-8967-946d6f098c6c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eDimension reduction with structure-aware quantum circuits for hybrid machine learning\u003c/p\u003e","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":"Quantum dimension reduction, quantum machine learning, Schmidt decomposition, quantum circuits","lastPublishedDoi":"10.21203/rs.3.rs-7264732/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7264732/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSchmidt decomposition of a vector can be understood as writing the singular value decomposition (SVD) in vector form. 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