Classical SU(2) Models Match or Exceed Shallow Variational Quantum Circuits on Classical Vision Benchmarks

Classical SU(2) Models Match or Exceed Shallow Variational Quantum Circuits on Classical Vision Benchmarks | 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 Classical SU(2) Models Match or Exceed Shallow Variational Quantum Circuits on Classical Vision Benchmarks Christopher Fulton, Irene Tsapara, Lawrence Fulton This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8501568/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 7 You are reading this latest preprint version Abstract Quaternion-valued neural networks and shallow variational quantum circuits (VQCs) both derive their local transformations from the rotation group SU(2), yet their comparative performance as learning architectures on classical supervised tasks has not been systematically examined. We present a controlled comparison in which real-valued, quaternion-valued, and quantum classifiers operate on identical frozen feature representations across MNIST, FashionMNIST, and CIFAR-10, isolating performance differences to the geometric inductive biases of the classification heads. For CIFAR-10, we evaluate two feature regimes—a learned 16-dimensional bottleneck and frozen ImageNet-pretrained ResNet18 features (512-dimensional)—to assess whether observed relationships reflect fundamental architectural properties or artifacts of representation capacity. Quaternion classifiers match real-valued baselines on MNIST (93.64% vs.93.54%) and FashionMNIST (84.47% vs. 84.60%), while shallow product-state VQCs achieve only 87.52% (MNIST) and 82.03% (FashionMNIST), despite substantially higher computational cost. On CIFAR-10, quaternion networks retain 94.3% of real-valued performance under the learned bottleneck and 95.9% under ResNet18 features, demonstrating robustness across a 32-fold increase in feature dimensionality. On CIFAR-10, product-state quantum circuits underperform quaternion classifiers by 2.8-3.5 percentage points across both feature regimes. Notably, entanglement reverses from providing modest gains (approximately +0.6 percentage points) on simple grayscale benchmarks to degrading performance by 9.3 percentage points relative to the product-state circuit when combined with high-quality pretrained features, indicating that additional quantum resources can adversely affect learning in shallow, measurement-limited regimes. These results demonstrate that classical SU(2) models realized through quaternion networks provide computationally efficient classification heads that match real-valued baselines while substantially outperforming shallow variational quantum circuits on classical vision tasks. Quaternion neural networks Variational quantum circuits SU(2) geometry Quantum machine learning Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 12 May, 2026 Reviews received at journal 06 May, 2026 Reviewers agreed at journal 26 Apr, 2026 Reviewers invited by journal 13 Mar, 2026 Editor assigned by journal 19 Feb, 2026 Submission checks completed at journal 05 Jan, 2026 First submitted to journal 02 Jan, 2026 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-8501568","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":593948270,"identity":"44914426-d774-441e-bd11-8c127b61259b","order_by":0,"name":"Christopher Fulton","email":"","orcid":"","institution":"United States Air Force Test Pilot School","correspondingAuthor":false,"prefix":"","firstName":"Christopher","middleName":"","lastName":"Fulton","suffix":""},{"id":593948271,"identity":"2261c4ff-89d2-4e3b-957d-7c497405f74c","order_by":1,"name":"Irene Tsapara","email":"","orcid":"","institution":"National University","correspondingAuthor":false,"prefix":"","firstName":"Irene","middleName":"","lastName":"Tsapara","suffix":""},{"id":593948272,"identity":"d0bd5af9-3235-447e-962a-4656632d8e83","order_by":2,"name":"Lawrence Fulton","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAApElEQVRIiWNgGAWjYBAC9gbmBiBlIWcA4vEQo4XnAGMjUI+EMelaEjcQr0Uisf3Bxx0S6dvZDzA+eNtGnJbGxplnJHJ39iQwG84lRos9UEszb5tE7oYbDGzSvMTaAtKSbnCDgf03SVoSgFrYmInTwvOwcebMNgnDnT2JzZJzzhGjhT35wIePbTby5uyHD354U0aEFiTA2ECa+lEwCkbBKBgFuAEAJbAzfOAe+LYAAAAASUVORK5CYII=","orcid":"","institution":"Boston College","correspondingAuthor":true,"prefix":"","firstName":"Lawrence","middleName":"","lastName":"Fulton","suffix":""}],"badges":[],"createdAt":"2026-01-02 14:24:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8501568/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8501568/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104781035,"identity":"b2ce805c-b4f4-43b7-8814-efb7da2302fd","added_by":"auto","created_at":"2026-03-17 07:54:32","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":506630,"visible":true,"origin":"","legend":"","description":"","filename":"Springer.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8501568/v1_covered_957a42a3-c60a-42bf-be0a-69c8da89cde4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Classical SU(2) Models Match or Exceed Shallow Variational Quantum Circuits on Classical Vision Benchmarks","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"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":"quantum-machine-intelligence","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"qumi","sideBox":"Learn more about [Quantum Machine Intelligence](http://link.springer.com/journal/42484)","snPcode":"42484","submissionUrl":"https://submission.nature.com/new-submission/42484/3","title":"Quantum Machine Intelligence","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Quaternion neural networks, Variational quantum circuits, SU(2) geometry, Quantum machine learning","lastPublishedDoi":"10.21203/rs.3.rs-8501568/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8501568/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Quaternion-valued neural networks and shallow variational quantum circuits (VQCs) both derive their local transformations from the rotation group SU(2), yet their comparative performance as learning architectures on classical supervised tasks has not been systematically examined. 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