A multi-axis diagnostic framework for Hybrid Quantum-Classical Neural Networks in Empirical setting

A multi-axis diagnostic framework for Hybrid Quantum-Classical Neural Networks in Empirical setting | 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 Article A multi-axis diagnostic framework for Hybrid Quantum-Classical Neural Networks in Empirical setting Praneel Gore This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7093575/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 Hybrid quantum-classical neural networks (HQNNs) are a promising paradigm in quantum enhaced machine learning, yet their evaluation remains an open challenge constrained by two key issues: reliance on single metrics (e.g., loss or gradients) and synthetic benchmarks that fail to reflect real-world complexities. This work introduces a multi-metric diagnostic framework, that offers a holistic view of HQNN behavior by analyzing primary axes: quantum trainability (gradient norms), model convergence (loss curves), and quantum utility (via the Quantum Contribution Score, QCS). And secondary axes: expressivity, gradient efficiency and entanglement entropy. Across 16 models over real-world and synthetic data with a classical artificial neural network as baseline. Through this framework empirical phenomena in practical evaluations are developed, including gradient recovery after barren plateaus, data and expressivity dependent QCS trends, relation between gradient behaviour and qubit to layer ratio and model convergence despite barren plateaus. Physical sciences/Mathematics and computing Physical sciences/Physics Full Text Additional Declarations Competing interest reported. The author declares a provisional patent application related to the research presented in this manuscript and intends to file a non-provisional patent application. 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-7093575","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":486384795,"identity":"887b43e6-b6de-4fc5-bb9b-81b19bb66c0c","order_by":0,"name":"Praneel Gore","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA50lEQVRIiWNgGAWjYPACCxDB+ABI8PARqUUCRDAbgLSwkaKFDUISUmsuffjZgw8VEnb90oePVX7NsZNhY2B++OgGHi2WfWnmhjPOSCTP7EtLuy27LRnoMDZj4xw8WgzOMJhJ87ZJJBuc4TG7LbmNGaiFh00avxb2b9J//4G08H8rltxWT4wWHjNpxgYJOyCDjfHjtsOEtVj28JRJ9hyTSJDsYTOWZtx2nIeNmYBfzHnYt0n8qLGx5+dhfvjx57Zqe3725oeP8ToMSic2AAlmHhCTGY9yZC32IILxBwHVo2AUjIJRMDIBAA7LPlHs6JELAAAAAElFTkSuQmCC","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Praneel","middleName":"","lastName":"Gore","suffix":""}],"badges":[],"createdAt":"2025-07-10 13:38:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7093575/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7093575/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":87629604,"identity":"3b8805ed-fda6-4cc2-b309-e0027d2c0ead","added_by":"auto","created_at":"2025-07-26 08:23:56","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5917689,"visible":true,"origin":"","legend":"","description":"","filename":"npjQIV10.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7093575/v1_covered_811b1db0-a76f-4b3b-8c4e-e4ca2e3af16d.pdf"}],"financialInterests":"Competing interest reported. 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