Prediction of the Ground State Energy of the Hydrogen Molecule using Quantum Neural Networks

Prediction of the Ground State Energy of the Hydrogen Molecule using Quantum Neural Networks | 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 Prediction of the Ground State Energy of the Hydrogen Molecule using Quantum Neural Networks Mohamed amine Hechmi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8084289/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 This paper addresses the challenge of accurately predicting the ground-state energy of the hydrogen molecule (H2), a fundamental problem in quantum chemistry that demands high precision and efficient computation. Traditional classical methods, such as Full Configuration Interaction (FCI), provide accurate results but are computationally expensive and scale poorly with system size. To overcome these limitations, we propose a hybrid quantum-classical approach based on Quantum Neural Networks (QNNs) trained on high-precision FCI data. Our method encodes interatomic distances into parameterized quantum circuits and employs classical optimization to learn the complex energy landscape of H2 across a wide range of molecular geometries. The QNN model achieves energy predictions that closely match reference FCI values with minimal deviation, while significantly reducing quantum resource requirements compared to conventional quantum algorithms. This work demonstrates the potential of QNNs as scalable and efficient tools for quantum chemistry, laying the groundwork for future applications to larger and more complex molecular systems. Quantum Neural Networks (QNN) Full Configuration Interaction (FCI) Hydrogen Molecule (H2) Ground State Energy Prediction Quantum Chemistry Simulation Hybrid QuantumClassical Methods Variational Quantum Algorithms Molecular Energy Landscape Quantum Machine Learning Parameterized Quantum Circuits Computational Chemistry Quantum Computing Applications Full Text Additional Declarations The authors declare no competing interests. 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. 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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-8084289","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":543170818,"identity":"d7be5f38-e97c-4447-9262-fc13f1d186ec","order_by":0,"name":"Mohamed amine Hechmi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFklEQVRIiWNgGAWjYFACHhDBDEYMjA0MDAYMjI0PSNbSbACVA/HxaGGAa2Fgk8CnRbe99+CnGxXW8rrtvAcfMO6wkTcXO9xW+bPtjjy/2AH2xwWYWszOnEuWzjmTbrjtMF+yAeOZNMOdsxPbbvO2PTOcOTuBsXkGFi03cgykc9sOM247zGMmwdh2OMHgNlALhAHUwoNVi/Hv3H+H7YFazH8wtv0Hayn8iV+LmXRuw+FEkC0MjG0HwFoYePFpOXPGzDrnWHoyUIuxRGJbsuGG24nN0jznQH5JbJyNTcvxHuPbOTXWttvOnzH88LHNTt7gdvrDjz/KgCEmnXzgMxYtqCABwTzAgDMmcYEDJKkeBaNgFIyCYQ0AqpFwtathgbYAAAAASUVORK5CYII=","orcid":"","institution":"university of carthage","correspondingAuthor":true,"prefix":"","firstName":"Mohamed","middleName":"amine","lastName":"Hechmi","suffix":""}],"badges":[],"createdAt":"2025-11-11 08:28:11","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-8084289/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8084289/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":95800915,"identity":"8119497c-f5b8-4d4e-a761-98fad6d44923","added_by":"auto","created_at":"2025-11-13 08:23:54","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":421819,"visible":true,"origin":"","legend":"","description":"","filename":"PredictionoftheGroundStateEnergyoftheHydrogenMoleculeusingQuantumNeuralNetworks.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8084289/v1_covered_c586fed6-6e6f-4ab8-9c8f-cbc8cefb5f2c.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003ePrediction of the Ground State Energy of the Hydrogen Molecule using Quantum Neural Networks\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Carthage","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"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 Neural Networks (QNN), Full Configuration Interaction (FCI), Hydrogen Molecule (H2), Ground State Energy Prediction, Quantum Chemistry Simulation, Hybrid QuantumClassical Methods, Variational Quantum Algorithms, Molecular Energy Landscape, Quantum Machine Learning, Parameterized Quantum Circuits, Computational Chemistry, Quantum Computing Applications","lastPublishedDoi":"10.21203/rs.3.rs-8084289/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8084289/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper addresses the challenge of accurately predicting the ground-state energy of the hydrogen molecule (H2), a fundamental problem in quantum chemistry that demands high precision and efficient computation. 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