A unified framework for efficient quantum simulation of nonlinear spectroscopy

A unified framework for efficient quantum simulation of nonlinear spectroscopy | 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 unified framework for efficient quantum simulation of nonlinear spectroscopy Xiao Yuan, Long Xiong, Xiaoyang Wang, Xiaoxia Cai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9298521/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is fundamentally limited by the exponential growth of the Hilbert space, and practical quantum algorithms for the nonlinear regime have remained largely unexplored. Here, we present a unified quantum algorithmic framework for computing n-th order nonlinear spectroscopies. By reformulating multi-time responses as a weighted sum of expectation values at finite pump amplitudes via a generalized parameter shift rule, our approach bypasses the costly evaluation of high-order commutators and time-dependent operator expansions. This reformulation enables efficient execution via real-time evolution on current quantum hardware, ensuring inherent noise resilience. We validate the framework on IBM's superconducting quantum processors, successfully obtain higher-order response functions of a 12-qubit XXZ spin-chain. Furthermore, the versatility of our method is demonstrated by resolving quasi-particle excitation spectra in spin-liquids and identifying interaction-induced cross-peaks in atomic systems. Our results establish a practical and scalable pathway for probing complex quantum dynamics on near-term quantum devices, extending the reach of quantum simulation into the nonlinear domain. Physical sciences/Physics/Quantum physics/Quantum simulation Physical sciences/Physics/Quantum physics/Quantum information Full Text Additional Declarations There is NO Competing Interest. Supplementary Files APPENDIXAunifiedframeworkforefficientquantumsimulationofnonlinearspectroscopy.pdf Supplementary Information Cite Share Download PDF Status: Under Review 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. 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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-9298521","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":624938892,"identity":"b78b73e1-8ce4-4b9a-9419-325da8fc63d6","order_by":0,"name":"Xiao Yuan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYDACZijNz8CGzCVGi2QD0VpgwOAAsVoMjjM/fMzbZpdnfLstTYKhwjqxgf3sAbxaJJvZjI1525KLze4cOybBcCY9sYEnLwGvFn5mBjNp3jbmxG030tskGNsOJzZI8Bjg1cLGzP4NqKU+cfMMkJZ/RGjhZ+YB2XI4cYNE2jEJxgYitEg28xQbzjl3PHHGnWPJFgnH0o3beHLwazE4f3zjgzdl1Yn9s9sMb3yosZbtZz+DXwsIMPGASAkgTgD5jqB6IGD8AdMyCkbBKBgFowAbAAAaVj7a//ojvwAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-0205-6545","institution":"Peking University","correspondingAuthor":true,"prefix":"","firstName":"Xiao","middleName":"","lastName":"Yuan","suffix":""},{"id":624938894,"identity":"f9d80654-e0f3-4d6a-8213-ecb2dd933d54","order_by":1,"name":"Long Xiong","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Long","middleName":"","lastName":"Xiong","suffix":""},{"id":624938895,"identity":"b27a7ff6-9265-4891-ab83-14961fc8c2cc","order_by":2,"name":"Xiaoyang Wang","email":"","orcid":"","institution":"RIKEN","correspondingAuthor":false,"prefix":"","firstName":"Xiaoyang","middleName":"","lastName":"Wang","suffix":""},{"id":624938896,"identity":"76afb5ca-171c-4e0f-8f04-b22e85aa2387","order_by":3,"name":"Xiaoxia Cai","email":"","orcid":"https://orcid.org/0000-0001-8791-8700","institution":"Institute of High Energy Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Xiaoxia","middleName":"","lastName":"Cai","suffix":""}],"badges":[],"createdAt":"2026-04-02 05:50:48","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9298521/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9298521/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107484620,"identity":"970b0df6-8dae-4614-b314-a6399f9667ab","added_by":"auto","created_at":"2026-04-22 02:32:32","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2214142,"visible":true,"origin":"","legend":"Article File","description":"","filename":"Aunifiedframeworkforefficientquantumsimulationofnonlinearspectroscopy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9298521/v1_covered_107b3a28-bf97-4405-8283-0f91365d0197.pdf"},{"id":107306859,"identity":"6758ed51-1b4c-4e35-8df5-b61198d1fc82","added_by":"auto","created_at":"2026-04-20 08:29:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":2714563,"visible":true,"origin":"","legend":"Supplementary Information","description":"","filename":"APPENDIXAunifiedframeworkforefficientquantumsimulationofnonlinearspectroscopy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9298521/v1/425bab3e5d8f1919f0c0df70.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"A unified framework for efficient quantum simulation of nonlinear spectroscopy","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-9298521/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9298521/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. 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