Smolyak algorithm assisted robust control for quantum systems with uncertainties

Smolyak algorithm assisted robust control for quantum systems with uncertainties | 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 Smolyak algorithm assisted robust control for quantum systems with uncertainties Zigui Zhang, Zibo Miao, Yu Chen, Xiu-Hao Deng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5313186/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 Efficient and systematic numerical methods for robust control design are crucial in quantum systems due to inevitable uncertainties or disturbances. We propose a novel approach that models uncertainties as random variables and quantifies robustness using the expectation of infidelity. By reformulating the robustness measure as a weighted tensor product quadrature, we employ the Smolyak sparse grid algorithm to develop a parametric robust quantum control scheme. This scheme significantly reduces computational cost while improving accuracy. We demonstrate the effectiveness of our Smolyak algorithm assisted gradient-based methods including \textbf{smGOAT} and \textbf{smGRAPE} in robust control problems regarding state transfer and quantum gate realization, with ultrahigh fidelity and strong robustness achieved. Our results contribute to improving the reliability and security of quantum computing and communication systems in the presence of real-world imperfections. Physical sciences/Physics/Quantum physics/Quantum information Physical sciences/Physics/Quantum physics/Qubits quantum systems with uncertainties robust control Smolyak algorithm Full Text Additional Declarations No competing interests reported. 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-5313186","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":369406367,"identity":"c7865b64-2686-4c81-872f-aded0d9ddace","order_by":0,"name":"Zigui Zhang","email":"","orcid":"","institution":"Harbin Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Zigui","middleName":"","lastName":"Zhang","suffix":""},{"id":369406368,"identity":"25967ee3-0546-437a-9ad9-9cfa11a71c05","order_by":1,"name":"Zibo Miao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYDACZhBhcICBX4KxAcYlUovkDMbGBuK0QMABBoMbDIzEadFtZ3748EfBHTnj283tDxgqrBMb2M8ewKvF7DCbsYGEwTNjszsHgQ47k57YwJOXQEALg5mEgcHhxG03EhsbGNsOJzZI8BgQ0ML+TSIBqGXzDJCWf0Rp4TGTOADUskECpKWBOC3Fhg1Av0gAHTYj4Vi6cRtPDgEt549vfPjjzx05/hnpDz58qLGW7Wc/g18LKkgAYjYS1I+CUTAKRsEowAEAP61JbgRjPaoAAAAASUVORK5CYII=","orcid":"","institution":"Harbin Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Zibo","middleName":"","lastName":"Miao","suffix":""},{"id":369406369,"identity":"fe3caf5d-0a0d-4d93-ac6c-4aeb419f4a98","order_by":2,"name":"Yu Chen","email":"","orcid":"","institution":"Tencent","correspondingAuthor":false,"prefix":"","firstName":"Yu","middleName":"","lastName":"Chen","suffix":""},{"id":369406370,"identity":"398acf7a-56f9-4106-8977-3ed573691d07","order_by":3,"name":"Xiu-Hao Deng","email":"","orcid":"","institution":"Southern University of\nScience and Technology","correspondingAuthor":false,"prefix":"","firstName":"Xiu-Hao","middleName":"","lastName":"Deng","suffix":""}],"badges":[],"createdAt":"2024-10-22 15:53:13","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-5313186/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5313186/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":67797763,"identity":"9727c8e1-6f88-4e4c-b73c-a02d5a4a1da0","added_by":"auto","created_at":"2024-10-29 20:53:30","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":950858,"visible":true,"origin":"","legend":"","description":"","filename":"smROCNQI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5313186/v1_covered_cc09e82b-8f65-4d95-a5d7-980f5da62db7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Smolyak algorithm assisted robust control for quantum systems with uncertainties","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","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 systems with uncertainties, robust control, Smolyak algorithm","lastPublishedDoi":"10.21203/rs.3.rs-5313186/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5313186/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Efficient and systematic numerical methods for robust control design are crucial in quantum systems due to inevitable uncertainties or disturbances. 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