On Quantum Perceptron Learning via Quantum Search

On Quantum Perceptron Learning via Quantum Search | 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 On Quantum Perceptron Learning via Quantum Search Xiaoyu Sun, Mathieu Roget, Giuseppe Di Molfetta, Hachem Kadri This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7158340/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract With the growing interest in quantum machine learning, the perceptron, a fundamental building block in traditional machine learning, has emerged as a valuable model for exploring quantum advantages. In this work, we make two principal contributions. First, we revisit the \emph{quantum version space perceptron} algorithm proposed by \cite{kapoor2016quantum}, identifying and correcting a flawed complexity assumption. We prove that the complexity of the algorithm is dimension-dependent, which has significant implications for the feasibility of the sampling-based quantum perceptron algorithm in high-dimensional regimes. Second, we propose and analyse two \emph{quantum-enhanced} cutting-plane algorithms for perceptron learning. Specifically, we leverage established quantum tools like \emph{Grover's search} and \emph{quantum walk search} in these algorithms. We provide detailed algorithmic constructions, complexity analysis and comparison to their classical counterparts. Our results demonstrate how quantum resources can yield provable improvements in query complexity and arithmetic operations, providing constructive insights into the statistical efficiency of different perceptron models and offering new perspectives on quantum perceptron learning. Quantum machine learning Linear classification Perceptron learning Grover’s search Quantum walk search Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 31 Jan, 2026 Reviews received at journal 24 Jan, 2026 Reviewers agreed at journal 16 Dec, 2025 Reviews received at journal 01 Nov, 2025 Reviewers agreed at journal 02 Oct, 2025 Reviewers invited by journal 29 Sep, 2025 Editor assigned by journal 22 Jul, 2025 Submission checks completed at journal 21 Jul, 2025 First submitted to journal 18 Jul, 2025 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. 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