Learning Parameterized Quantum Circuits with Quantum Gradient

Learning Parameterized Quantum Circuits with Quantum Gradient | 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 Learning Parameterized Quantum Circuits with Quantum Gradient Keren Li, Yuanfeng Wang, Pan Gao, Shenggen Zheng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5649913/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 Feb, 2026 Read the published version in npj Quantum Information → Version 1 posted 8 You are reading this latest preprint version Abstract Parameterized quantum circuits (PQCs) are crucial for quantum machine learning and circuit synthesis, enabling the practical implementation of complex quantum tasks. However, PQC learning has been largely confined to classical optimization methods, which suffer from issues like gradient vanishing.In this work, we introduce a nested optimization model, a hybrid approach that leverages quantum gradients to improve PQC learning for arbitrary polynomial-type cost functions. The proposed approach decomposes the learning problem into multiple subproblems, each aimed at learning the state identified by the quantum gradient using current circuit synthesis methods.By leveraging quantum gradients, the optimization procedure is free of a specific type of gradient vanishing, such as unfavorable local stationary points and barren plateaus.Specifically, with the guidance of quantum gradient, unfavorable local stationary points can be overcome by increasing the depth of the ansatz, while barren plateaus can be mitigated by constraining the optimization region.Numerically, we demonstrate the feasibility of the approach on two tasks: the Max-Cut problem and polynomial optimization. Additionally, we analyze the overheads introduced by this approach, which are primarily polynomial in the number of qubits in the system and can be controlled by adjusting the learning rate.The method can generate circuits while avoiding gradient vanishing, thus effectively optimizing the cost function.From the perspective of quantum algorithms, our model improves quantum optimization for polynomial-type cost functions, addressing the challenge of exponential sample complexity growth. Physical sciences/Physics/Quantum physics/Quantum information Physical sciences/Physics Physical sciences/Physics/Information theory and computation Full Text Additional Declarations No competing interests reported. Supplementary Files SupplementaryInformation.pdf Cite Share Download PDF Status: Published Journal Publication published 25 Feb, 2026 Read the published version in npj Quantum Information → Version 1 posted Editorial decision: Revision requested 12 Sep, 2025 Reviews received at journal 20 Aug, 2025 Reviewers agreed at journal 19 Aug, 2025 Reviews received at journal 05 May, 2025 Reviewers agreed at journal 15 Apr, 2025 Reviewers invited by journal 15 Apr, 2025 Submission checks completed at journal 08 Apr, 2025 First submitted to journal 31 Mar, 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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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-5649913","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":443380914,"identity":"1d706ecf-0c97-4edf-bcb8-07bb65ee9334","order_by":0,"name":"Keren Li","email":"","orcid":"","institution":"College of Physics and Optoelectronic Engineering, Shenzhen University","correspondingAuthor":false,"prefix":"","firstName":"Keren","middleName":"","lastName":"Li","suffix":""},{"id":443380915,"identity":"0fcd0943-cf63-4593-a9fe-55b8824cbd03","order_by":1,"name":"Yuanfeng Wang","email":"","orcid":"","institution":"Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)","correspondingAuthor":false,"prefix":"","firstName":"Yuanfeng","middleName":"","lastName":"Wang","suffix":""},{"id":443380916,"identity":"0d605416-a14e-4a75-ada3-13b49588f084","order_by":2,"name":"Pan Gao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAz0lEQVRIiWNgGAWjYPACmwQGBsYGkrSkka7lcALxauXdDx978HPH+Tz+9uTmDww1dgz8swnYZngmLd2w98ztYokzD9skGI4lM0jcOUBAS0OOmQRv2+3EhhuJbQwMbAcYDCQIONKw/42Z5N+2c4nzbyQCHfaPCC3yEjlm0rxtBxI33EhskGBsI0KLgcSzdGPZtuRiQ5BfEvuSeSRuELKlP/nYw7dtdnlyx9Mff/jwzU6OfwYhWw4wsEGZCWDEg189yJYGZC2jYBSMglEwCrABAOGCRkVO86Q6AAAAAElFTkSuQmCC","orcid":"","institution":"Beijing Academy of Quantum Information Sciences","correspondingAuthor":true,"prefix":"","firstName":"Pan","middleName":"","lastName":"Gao","suffix":""},{"id":443380917,"identity":"88f985a5-8eae-4c23-8f5b-052f22173c36","order_by":3,"name":"Shenggen Zheng","email":"","orcid":"","institution":"Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)","correspondingAuthor":false,"prefix":"","firstName":"Shenggen","middleName":"","lastName":"Zheng","suffix":""}],"badges":[],"createdAt":"2024-12-16 02:38:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5649913/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5649913/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41534-025-01179-7","type":"published","date":"2026-02-25T15:58:57+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":103765821,"identity":"4dae8e26-61ec-4a1a-b678-7ef573fe5029","added_by":"auto","created_at":"2026-03-02 16:09:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":700917,"visible":true,"origin":"","legend":"","description":"","filename":"NOMrevised.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5649913/v1_covered_d431a512-9e82-40b9-ab40-b5b20e4ff7f3.pdf"},{"id":80707550,"identity":"e8fabfd2-c7bf-48fa-876f-1d56c55c85b0","added_by":"auto","created_at":"2025-04-16 08:47:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1875688,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryInformation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5649913/v1/2c6d1043adb3bb01a125720b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Learning Parameterized Quantum Circuits with Quantum Gradient","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-5649913/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5649913/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Parameterized quantum circuits (PQCs) are crucial for quantum machine learning and circuit synthesis, enabling the practical implementation of complex quantum tasks. 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