Quantum2Prompt: Representing Quantum Circuits as Language Prompts for Linear System Solving

Quantum2Prompt: Representing Quantum Circuits as Language Prompts for Linear System Solving | 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 Quantum2Prompt: Representing Quantum Circuits as Language Prompts for Linear System Solving Youla Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8187619/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 We present Quantum2Prompt , a cross-modal framework that reformulates quantum circuits as structured language prompts, enabling large language models (LLMs) to estimate outcomes of the Variational Quantum Linear Solver (VQLS). Instead of relying on iterative quantum--classical loops with repeated measurements, Quantum2Prompt translates gate sequences, control--target relations, and rotation parameters into compact textual descriptions that preserve circuit semantics while remaining hardware-agnostic. An LLM-based regressor consumes these descriptions to produce real-valued residual estimates, transforming VQLS outcome prediction into a prompt-to-residual regression task. Extensive experiments across Toeplitz, Laplacian, and sparse matrix families show that Quantum2Prompt achieves up to \((R^2 = 0.99)\) and MSE = 0.0026 , substantially outperforming classical baselines such as Random Forest, SVR, and LightGBM. Ablation and noise-robustness analyses further demonstrate that combining circuit text, rotation parameters, and optimization-step features yields the most accurate and noise-resilient predictions. Beyond empirical gains, we contribute the first benchmark dataset aligning VQLS circuits, textual encodings, and residual labels, enabling reproducible evaluation and hybrid quantum--language workflows. These results suggest that LLMs can serve as efficient, interpretable surrogates for variational solvers, paving the way toward language-driven quantum algorithm design and performance prediction.The full dataset and implementation are publicly available for reproducibility. Quantum machine learning Variational quantum algorithms Language models Surrogate modeling Quantum2Prompt VQLS Cross-modal regression 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. 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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-8187619","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":549816126,"identity":"f095bfd1-c7d3-4576-843a-f6d58295b188","order_by":0,"name":"Youla Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtElEQVRIiWNgGAWjYBADGX5mEMVGghYeyWaStRgcIFaLwfGzh1/zVBzmMT7OY8DwoewwEVrO5KVZ85w5zGN2mMeAccY5YrQcyDEz5m2DaGEGMojQcv4NRItxM1DLX6K03MgxfgzSYsAMRIzEaJG88caMcc6ZdB6Jw2wFB3vOpRPWwnc+x/jDmwprOf7+wxsf/CizJqxF4QADmxQPlHOAsHogkG9gYP74gyilo2AUjIJRMGIBAI94OEXwR02uAAAAAElFTkSuQmCC","orcid":"","institution":"Indiana University Bloomington Department of Intelligent Systems Engineering","correspondingAuthor":true,"prefix":"","firstName":"Youla","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2025-11-23 20:53:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8187619/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8187619/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101753781,"identity":"a4226a09-d13a-4d42-9d3a-f00c4e4ad2dd","added_by":"auto","created_at":"2026-02-03 10:40:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":287830,"visible":true,"origin":"","legend":"","description":"","filename":"Quantum2PromptRepresentingQuantumCircuitsasLanguagePromptsforLinearSystemSolving6.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8187619/v1_covered_25faca44-5500-4f1c-9aab-674aadb6b384.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Quantum2Prompt: Representing Quantum Circuits as Language Prompts for Linear System Solving","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, Variational quantum algorithms, Language models, Surrogate modeling, Quantum2Prompt, VQLS, Cross-modal regression","lastPublishedDoi":"10.21203/rs.3.rs-8187619/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8187619/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe present \u003cb\u003eQuantum2Prompt\u003c/b\u003e, a cross-modal framework that reformulates quantum circuits as structured language prompts, enabling large language models (LLMs) to estimate outcomes of the Variational Quantum Linear Solver (VQLS). Instead of relying on iterative quantum--classical loops with repeated measurements, Quantum2Prompt translates gate sequences, control--target relations, and rotation parameters into compact textual descriptions that preserve circuit semantics while remaining hardware-agnostic. An LLM-based regressor consumes these descriptions to produce real-valued residual estimates, transforming VQLS outcome prediction into a \u003cem\u003eprompt-to-residual regression\u003c/em\u003e task. Extensive experiments across Toeplitz, Laplacian, and sparse matrix families show that Quantum2Prompt achieves up to \u003cb\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((R^2 = 0.99)\\)\u003c/span\u003e\u003c/span\u003e\u003c/b\u003e and \u003cb\u003eMSE = 0.0026\u003c/b\u003e, substantially outperforming classical baselines such as Random Forest, SVR, and LightGBM. Ablation and noise-robustness analyses further demonstrate that combining circuit text, rotation parameters, and optimization-step features yields the most accurate and noise-resilient predictions. Beyond empirical gains, we contribute the first benchmark dataset aligning VQLS circuits, textual encodings, and residual labels, enabling reproducible evaluation and hybrid quantum--language workflows. 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