Q-TAILOR: Tail-Adaptive Quantum Operator Learning for Protein Structure Refinement

Q-TAILOR: Tail-Adaptive Quantum Operator Learning for Protein Structure Refinement | 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 Q-TAILOR: Tail-Adaptive Quantum Operator Learning for Protein Structure Refinement Parham Ghayour This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8415175/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 Protein structure refinement is inherently a tail-dominated problem: only a small fraction of conformations lie near the native basin, yet reliable improvement in this regime is critical for downstream accuracy. Most existing learning-based approaches address refinement indirectly through energy prediction or ranking, optimizing average performance rather than worst-case behavior. As a result, difficult near-native conformations often remain poorly treated. In this work, we introduce Q-TAILOR, a tail-adaptive operator learning framework for protein structure refinement. Q-TAILOR formulates refinement as the learning of a structured transformation on conformation space, explicitly optimized for worst-case improvement using a Conditional Value-at-Risk (CVaR) objective. The refinement operator is constrained to a low-rank geometric subspace and parameterized via a nonlinear coefficient generator in spired by quantum expectation values, enabling expressive yet stable refine ment dynamics. An ambiguity-driven adaptive mechanism allocates expres sive capacity selectively to difficult conformations, mitigating optimization pathologies associated with uniformly deep models. We provide theoretical analysis showing that operator learning is better conditioned than scalar energy prediction in tail-dominated landscapes and that CVaR induces gradient concentration on the most informative refinement cases. Controlled experiments on a synthetic refinement task demonstrate that Q-TAILOR achieves substantially stronger improvements in the tail of the quality distribution than in the mean, while maintaining stable refinement across all inputs. Although evaluated in a minimal setting, the results validate the central premise of the approach: reliable protein refinement requires tail-sensitive op erator learning rather than average-case prediction. Q-TAILOR establishes a general framework that can be extended to higher-dimensional protein models and hybrid classical–quantum implementations as computational resources mature Quantum Machine Learning Protein Folding Variational Quantum Circuits CVaR Operator Learning Structural Refinement 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-8415175","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":563551470,"identity":"7dd280f7-f829-4429-b7b2-ca414bd2bff3","order_by":0,"name":"Parham Ghayour","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0001-5607-1532","institution":"Sorbonne university","correspondingAuthor":true,"prefix":"","firstName":"Parham","middleName":"","lastName":"Ghayour","suffix":""}],"badges":[],"createdAt":"2025-12-21 04:39:46","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-8415175/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8415175/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99788108,"identity":"d4463301-3b80-4f10-85aa-e607de7f12af","added_by":"auto","created_at":"2026-01-08 12:44:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":417284,"visible":true,"origin":"","legend":"","description":"","filename":"quantumMLproteinfoldingtaylornew.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8415175/v1_covered_3d691494-3823-4703-9bc4-71bf43c6adfb.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eQ-TAILOR: Tail-Adaptive Quantum Operator Learning for Protein Structure Refinement\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"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":"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 Machine Learning, Protein Folding, Variational Quantum Circuits, CVaR, Operator Learning, Structural Refinement","lastPublishedDoi":"10.21203/rs.3.rs-8415175/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8415175/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eProtein structure refinement is inherently a tail-dominated problem: only a small fraction of conformations lie near the native basin, yet reliable improvement in this regime is critical for downstream accuracy. Most existing learning-based approaches address refinement indirectly through energy prediction or ranking, optimizing average performance rather than worst-case behavior. As a result, difficult near-native conformations often remain poorly treated. In this work, we introduce Q-TAILOR, a tail-adaptive operator learning framework for protein structure refinement. Q-TAILOR formulates refinement as the learning of a structured transformation on conformation space, explicitly optimized for worst-case improvement using a Conditional Value-at-Risk (CVaR) objective. The refinement operator is constrained to a low-rank geometric subspace and parameterized via a nonlinear coefficient generator in spired by quantum expectation values, enabling expressive yet stable refine ment dynamics. An ambiguity-driven adaptive mechanism allocates expres sive capacity selectively to difficult conformations, mitigating optimization pathologies associated with uniformly deep models. We provide theoretical analysis showing that operator learning is better conditioned than scalar energy prediction in tail-dominated landscapes and that CVaR induces gradient concentration on the most informative refinement cases. Controlled experiments on a synthetic refinement task demonstrate that Q-TAILOR achieves substantially stronger improvements in the tail of the quality distribution than in the mean, while maintaining stable refinement across all inputs. Although evaluated in a minimal setting, the results validate the central premise of the approach: reliable protein refinement requires tail-sensitive op erator learning rather than average-case prediction. 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