Polynomially efficient quantum enabled variational Monte Carlo for training neural-network quantum states for physico-chemical applications

Polynomially efficient quantum enabled variational Monte Carlo for training neural-network quantum states for physico-chemical applications | 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 Polynomially efficient quantum enabled variational Monte Carlo for training neural-network quantum states for physico-chemical applications Manas Sajjan, Vinit Singh, Sabre Kais This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8887785/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract With diverse architectures and strong expressivity, neural-network quantum states (NQS) offer an alternative to traditional variational ansätze for simulating physical systems. Energy-based models such as Hopfield networks and Restricted Boltzmann Machines draw on statistical physics, mapping quantum states onto energy landscapes as associative memories. We show these models can be trained efficiently with Monte Carlo accelerated by quantum devices. Our algorithm scales linearly with circuit width and depth, uses constant measurements, avoids mid-circuit measurements, and requires polynomial storage. It treats both phase and amplitude fields, enlarging the trial space. Sampling on quantum hardware shortens mixing times and yields more faithful estimates, revealing a quantum-assisted advantage. We demonstrate accurate learning of ground states for local spin models and nonlocal electronic-structure Hamiltonians, including at distorted geometries with strong multi-reference correlation. Benchmarks show close agreement and high robustness highlighting promise of machine-learning protocols paired with near-term quantum devices for state learning in chemistry and condensed-matter physics. Physical sciences/Mathematics and computing Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Supplementary Files SuppInfounmarked.pdf Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 20 Mar, 2026 Reviewers agreed at journal 09 Mar, 2026 Reviewers agreed at journal 09 Mar, 2026 Reviewers invited by journal 09 Mar, 2026 Editor assigned by journal 22 Feb, 2026 Submission checks completed at journal 22 Feb, 2026 First submitted to journal 15 Feb, 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. 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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-8887785","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":603452483,"identity":"3df71cd3-1984-4fa2-a2cb-c6aaac5ee4d4","order_by":0,"name":"Manas Sajjan","email":"","orcid":"","institution":"North Carolina State University","correspondingAuthor":false,"prefix":"","firstName":"Manas","middleName":"","lastName":"Sajjan","suffix":""},{"id":603452484,"identity":"6bc4325e-fd77-40ae-8522-86b248178dad","order_by":1,"name":"Vinit Singh","email":"","orcid":"","institution":"North Carolina State University","correspondingAuthor":false,"prefix":"","firstName":"Vinit","middleName":"","lastName":"Singh","suffix":""},{"id":603452485,"identity":"a81801b2-c956-491b-b5cd-70174cf64048","order_by":2,"name":"Sabre Kais","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsUlEQVRIiWNgGAWjYDACHgaGAwwVCA6xWs6QqoWBsY0ULfI9hx8e/Dnvjrz8jATGB2/bCOtgMDjbZnCYd9szww03EpgN5xKlhZ/B4DDjtsMJBhIJbNK8xGiR72f/cPDnnMMJQIex/yZKC8PZHoMDvA2HExhuJLAxE6XF4MyZgsM8xw4bbjjzsFlyzjliHNaTvvnjj5rD8vLtyQc/vCkjxmEIwNhAmvpRMApGwSgYBbgBAEOjOPwisdOUAAAAAElFTkSuQmCC","orcid":"","institution":"North Carolina State University","correspondingAuthor":true,"prefix":"","firstName":"Sabre","middleName":"","lastName":"Kais","suffix":""}],"badges":[],"createdAt":"2026-02-15 18:08:49","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8887785/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8887785/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104782394,"identity":"61c82217-602a-463e-be31-891073664876","added_by":"auto","created_at":"2026-03-17 07:57:14","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2857688,"visible":true,"origin":"","legend":"","description":"","filename":"npjmainmanuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8887785/v1_covered_4730cc14-cebc-4389-95c0-a9b89d319447.pdf"},{"id":104605741,"identity":"8dcd6ea6-beb6-4cd3-a6fe-259fd38bed06","added_by":"auto","created_at":"2026-03-14 00:03:24","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":2469625,"visible":true,"origin":"","legend":"","description":"","filename":"SuppInfounmarked.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8887785/v1/9bc11618534b338316cc19cb.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Polynomially efficient quantum enabled variational Monte Carlo for training neural-network quantum states for physico-chemical applications","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-quantum-information","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjqi","sideBox":"Learn more about [npj Quantum Information](http://www.nature.com/npjqi/)","snPcode":"41534","submissionUrl":"https://mts-npjqi.nature.com/","title":"npj Quantum Information","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8887785/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8887785/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"With diverse architectures and strong expressivity, neural-network quantum states (NQS) offer an alternative to traditional variational ansätze for simulating physical systems. 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