Calibration-Aware Graph Neural Networks for Robust and Scalable Quantum Error Mitigation

Calibration-Aware Graph Neural Networks for Robust and Scalable Quantum Error Mitigation | 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 Short Report Calibration-Aware Graph Neural Networks for Robust and Scalable Quantum Error Mitigation Shen Zhihao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8236164/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 Noisy Intermediate-Scale Quantum (NISQ) computing is fundamentally constrained by hardware noise that is not only large but also temporally drifting and structurally complex. Traditional quantum error mitigation (QEM) techniques, such as Zero-Noise Extrapolation (ZNE), often rely on simplified noise assumptions that degrade under coherent errors and deep circuit structures. Conversely, existing machine learning-based QEM approaches typically treat device noise as a static background, leading to poor generalization when hardware calibration shifts. In this work, we propose \textbf{Calib-GNN}, a novel framework that explicitly integrates real-time hardware calibration data into a Graph Neural Network (GNN) architecture. By embedding gate-specific error rates directly into the graph representation, our model learns a dynamic mapping from noisy measurements to ideal expectation values. Through extensive simulations based on real noise profiles from the IBM Quantum \texttt{ibm\_fez} backend, we demonstrate that Calib-GNN significantly outperforms standard baselines. Specifically, it reduces the Root Mean Square Error (RMSE) by approximately 14\% compared to ZNE on random circuits and exhibits superior robustness against severe noise drift where traditional models fail. Furthermore, we show that Calib-GNN effectively scales to deeper circuits and recovers the ground state energy of the $H_2$ molecule in Variational Quantum Eigensolver (VQE) tasks with high fidelity, overcoming the limitations of ZNE in the presence of coherent noise. Computational Physics 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. 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-8236164","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Short Report","associatedPublications":[],"authors":[{"id":552612092,"identity":"7bdfdd50-3f82-4381-9459-35350a61e610","order_by":0,"name":"Shen Zhihao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEUlEQVRIiWNgGAWjYBACfvmDDQcSDCTs+PmbD4BFJEAEDx4tkjOYDx54UGCRLDnjWALDAWK0GNxgSz744EMF44YDOQbEaWG43WMAchizwYEznz9/bGPIk5yRwPjgbRuDvDkOHYxzzoC18Eke7t0mcbCNoVhaIoHZcG4bg+HOBuxamBlyILbwHTi7jQGoJXGeRAKbNG8bQ4LBAexa2KBaGBsO5Dz+ANXC/hufFh6JtASwlgkHchhADkucDbSFGZ8WCZ7DB0BaQIFsJnHmnESxZM/DZsk55yQMN+DQYn+8sfnjjz91oKh8/KGizCZP4njywQ9vymzkcdmCYWsCMBQbGKDRQxxIIF7pKBgFo2AUjBQAACgmY/pSkNOkAAAAAElFTkSuQmCC","orcid":"","institution":"School of Advanced Materials, Peking University Shenzhen Graduate School","correspondingAuthor":true,"prefix":"","firstName":"Shen","middleName":"","lastName":"Zhihao","suffix":""}],"badges":[],"createdAt":"2025-11-29 10:04:12","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-8236164/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8236164/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":97249800,"identity":"f29e2375-5ce8-4b77-bffe-71fba2228ed5","added_by":"auto","created_at":"2025-12-02 13:13:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":608917,"visible":true,"origin":"","legend":"","description":"","filename":"FormattingInstructionsforICLR2025ConferenceSubmissions12.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8236164/v1_covered_ff6b3eec-d4f3-404e-be6e-2974c12cd59e.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eCalibration-Aware Graph Neural Networks for Robust and Scalable Quantum Error Mitigation\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Peking University","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":"","lastPublishedDoi":"10.21203/rs.3.rs-8236164/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8236164/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNoisy Intermediate-Scale Quantum (NISQ) computing is fundamentally constrained by hardware noise that is not only large but also temporally drifting and structurally complex. Traditional quantum error mitigation (QEM) techniques, such as Zero-Noise Extrapolation (ZNE), often rely on simplified noise assumptions that degrade under coherent errors and deep circuit structures. Conversely, existing machine learning-based QEM approaches typically treat device noise as a static background, leading to poor generalization when hardware calibration shifts. In this work, we propose \\textbf{Calib-GNN}, a novel framework that explicitly integrates real-time hardware calibration data into a Graph Neural Network (GNN) architecture. By embedding gate-specific error rates directly into the graph representation, our model learns a dynamic mapping from noisy measurements to ideal expectation values. Through extensive simulations based on real noise profiles from the IBM Quantum \\texttt{ibm\\_fez} backend, we demonstrate that Calib-GNN significantly outperforms standard baselines. Specifically, it reduces the Root Mean Square Error (RMSE) by approximately 14\\% compared to ZNE on random circuits and exhibits superior robustness against severe noise drift where traditional models fail. Furthermore, we show that Calib-GNN effectively scales to deeper circuits and recovers the ground state energy of the $H_2$ molecule in Variational Quantum Eigensolver (VQE) tasks with high fidelity, overcoming the limitations of ZNE in the presence of coherent noise.\u003c/p\u003e","manuscriptTitle":"Calibration-Aware Graph Neural Networks for Robust and Scalable Quantum Error Mitigation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-02 07:10:35","doi":"10.21203/rs.3.rs-8236164/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"410ad025-0068-4344-a7ea-16dc4b9ec15a","owner":[],"postedDate":"December 2nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":58811673,"name":"Computational Physics"}],"tags":[],"updatedAt":"2025-12-02T07:10:35+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-02 07:10:35","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8236164","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8236164","identity":"rs-8236164","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}