Variational Quantum Algorithms for Image Classification

Variational Quantum Algorithms for Image Classification | 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Article Variational Quantum Algorithms for Image Classification Andrej Sum-Shik, Peter Thoma This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9349408/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 algorithms are among the most widely studied approaches for applying near-term quantum devices to learning tasks. In this work we investigate a supervised quantum-autoencoder-style classifier that encodes images by amplitude encoding and predicts labels from a designated readout sub-register. Building on the quantum-autoencoder (QAE)-style classifier of Asaoka and Kudo, we make three contributions. First, we give a rigorous equivalence result showing that, for computational-basis label states, the original SWAP-test-based training objective can be estimated without ancilla and reference registers by directly measuring the readout subsystem. This simplification reduces circuit resources while preserving the same training signal. Second, we propose a lightweight hybrid extension: instead of using only the probability of the correct readout bitstring, we estimate the full readout distribution and apply a learnable temperature-and-bias post-processing followed by a softmax normalization. Across MNIST, KMNIST, and Fashion-MNIST (restricted to eight classes), this classical post-processing yields substantial and statistically significant improvements in evaluation accuracy, consistently across cross-entropy and mean-squared-error objectives. Finally, to interpret these gains we analyze Fisher-geometry summaries based on effective dimension and complementary Fisher-spectrum diagnostics for both the quantum models and the classical baselines. Empirically, the hybrid quantum model is associated with a more spectrally concentrated and anisotropic Fisher geometry, with Fisher mass concentrated in fewer dominant directions and with a substantially larger local Fisher scale after training. Quantum machine learning Variational quantum algorithms Quantum autoencoder Image classification Hybrid quantum--classical models Effective dimension 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. 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-9349408","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":619942624,"identity":"3858fcaf-8c35-4690-9a82-13e6aebedc77","order_by":0,"name":"Andrej Sum-Shik","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYLACxgYJA34QI6GAFC2SDSAtBsRrYTAwOABiEaOFv/+M6cafOyyMjc+vTvzwwIBBnl/sAH4tEjdyzG7znpEwM7vxdrME0GGGM2cnELDmBo/ZbcY2CRuzG2c3gLQkGNwmoEX+/Bmzmz+BWoxnnN38gygtBgdyzG7wtkmYGfD3biPOFsMbaWW3gVqMJW7wbrNIMJAg7Be584e3AR1WZ9jff3bzzR8VNvL80gS0IIAEWKUEscpBgP8AKapHwSgYBaNgJAEARmJFb77NBxkAAAAASUVORK5CYII=","orcid":"","institution":"Frankfurt University of Applied Sciences","correspondingAuthor":true,"prefix":"","firstName":"Andrej","middleName":"","lastName":"Sum-Shik","suffix":""},{"id":619942634,"identity":"89fa8b21-6e58-49b3-8efd-3a2fa4753108","order_by":1,"name":"Peter Thoma","email":"","orcid":"","institution":"Frankfurt University of Applied Sciences","correspondingAuthor":false,"prefix":"","firstName":"Peter","middleName":"","lastName":"Thoma","suffix":""}],"badges":[],"createdAt":"2026-04-07 21:23:36","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9349408/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9349408/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106961264,"identity":"3389bd13-a795-4e92-8edd-89f3985c727c","added_by":"auto","created_at":"2026-04-15 09:24:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":684257,"visible":true,"origin":"","legend":"","description":"","filename":"VariationalQuantumAlgorithmsforImageClassification.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9349408/v1_covered_8fbe7369-e479-4827-b0b5-1701b8dc5fa7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Variational Quantum Algorithms for Image Classification","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 machine learning, Variational quantum algorithms, Quantum autoencoder, Image classification, Hybrid quantum--classical models, Effective dimension","lastPublishedDoi":"10.21203/rs.3.rs-9349408/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9349408/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eVariational quantum algorithms are among the most widely studied approaches for applying near-term quantum devices to learning tasks. 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