When Is a Probabilistic Qubit Model Valid? Subspace Leakage as a Quantitative Diagnostic for Quantum Architectures

When Is a Probabilistic Qubit Model Valid? Subspace Leakage as a Quantitative Diagnostic for Quantum Architectures | 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 When Is a Probabilistic Qubit Model Valid? Subspace Leakage as a Quantitative Diagnostic for Quantum Architectures Kyuhyung Choi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8737431/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Probabilistic qubit models are indispensable tools in quantum engineering, yet their domain of validity is often assumed rather than explicitly examined. Standard reduced descriptions, including Lindblad master equations, Pauli error channels, and fidelity-based benchmarks, implicitly rely on the assumption that non-computational dynamics remain negligible. In realistic devices, however, physical qubits are embedded in larger Hilbert spaces, and leakage into non-computational degrees of freedom can invalidate these approximations. In this work, I present a minimal, matrix-based framework that treats subspace leakage as a quantitative diagnostic for the validity of probabilistic qubit models. Qubits are defined as projected subspaces of a global state space, and leakage is quantified by the population residing outside the computational subspace. Rather than addressing the origin of quantum probability, the framework focuses on identifying when reduced probabilistic descriptions remain controlled approximations and when higher-dimensional models become necessary. To make this notion concrete, a phenomenological leakage model is applied to a distance-3 rotated surface code. A code-dependent leakage tolerance, ε_QEC, is derived using a two-fold logical error degradation criterion. The resulting tolerance is found to lie on the order of 10⁻⁴ per cycle and depends strongly on whether leakage predominantly affects measurement processes or manifests as data errors, spanning nearly a factor of four for fixed code distance. This sensitivity is not captured by fidelity-based metrics alone. By providing an explicit validity condition for reduced probabilistic models, this work complements existing benchmarks and introduces isolation as an independent diagnostic axis. The framework is broadly applicable across qubit platforms and error-correcting codes, clarifying when probabilistic modeling assumptions in quantum hardware design remain justified. Quantum engineering Leakage error Model validity Surface code Error correction assumptions Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 12 Mar, 2026 Editor assigned by journal 02 Feb, 2026 Submission checks completed at journal 02 Feb, 2026 First submitted to journal 30 Jan, 2026 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-8737431","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":605214176,"identity":"4ce51c99-a255-47cd-95e4-057b9ca2a268","order_by":0,"name":"Kyuhyung Choi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwElEQVRIiWNgGAWjYBACCQi2gfETiNaSRrqWwyRokZyRY3jjR815e3OJBMYPPxjS8glqkZbIMbbsOXY7ceeMBGbJHoYcywZCWuQkcswkeBtuJxjcSGCQZmCoMCBoC0iL5N+Gc/ZALcy/idICdJiZNG/DAcYNNxLYgLbkENYi2fOs2FrmWHLihjMP2yx7DNIIa5E4nrzx5psaO3uD48mHb/yoSCashUEgAcZibGBgIEIDAwP/AWJUjYJRMApGwYgGABJDNncqUgjGAAAAAElFTkSuQmCC","orcid":"","institution":"Catholic University of Korea","correspondingAuthor":true,"prefix":"","firstName":"Kyuhyung","middleName":"","lastName":"Choi","suffix":""}],"badges":[],"createdAt":"2026-01-30 05:38:48","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8737431/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8737431/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104721779,"identity":"9fa2da2f-7b6a-4417-8e5b-8b224f0089b4","added_by":"auto","created_at":"2026-03-16 12:27:30","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":420671,"visible":true,"origin":"","legend":"","description":"","filename":"QIPmanuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8737431/v1_covered_c7881d13-318f-4159-8eef-4add7d770d17.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"When Is a Probabilistic Qubit Model Valid? Subspace Leakage as a Quantitative Diagnostic for Quantum Architectures","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"quantum-information-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"qinp","sideBox":"Learn more about [Quantum Information Processing](http://link.springer.com/journal/11128)","snPcode":"11128","submissionUrl":"https://submission.nature.com/new-submission/11128/3","title":"Quantum Information Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Quantum engineering, Leakage error, Model validity, Surface code, Error correction assumptions","lastPublishedDoi":"10.21203/rs.3.rs-8737431/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8737431/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eProbabilistic qubit models are indispensable tools in quantum engineering, yet their domain of validity is often assumed rather than explicitly examined. Standard reduced descriptions, including Lindblad master equations, Pauli error channels, and fidelity-based benchmarks, implicitly rely on the assumption that non-computational dynamics remain negligible. In realistic devices, however, physical qubits are embedded in larger Hilbert spaces, and leakage into non-computational degrees of freedom can invalidate these approximations.\u003c/p\u003e \u003cp\u003eIn this work, I present a minimal, matrix-based framework that treats subspace leakage as a quantitative diagnostic for the validity of probabilistic qubit models. Qubits are defined as projected subspaces of a global state space, and leakage is quantified by the population residing outside the computational subspace. Rather than addressing the origin of quantum probability, the framework focuses on identifying when reduced probabilistic descriptions remain controlled approximations and when higher-dimensional models become necessary.\u003c/p\u003e \u003cp\u003eTo make this notion concrete, a phenomenological leakage model is applied to a distance-3 rotated surface code. A code-dependent leakage tolerance, ε_QEC, is derived using a two-fold logical error degradation criterion. The resulting tolerance is found to lie on the order of 10⁻⁴ per cycle and depends strongly on whether leakage predominantly affects measurement processes or manifests as data errors, spanning nearly a factor of four for fixed code distance. This sensitivity is not captured by fidelity-based metrics alone.\u003c/p\u003e \u003cp\u003eBy providing an explicit validity condition for reduced probabilistic models, this work complements existing benchmarks and introduces isolation as an independent diagnostic axis. The framework is broadly applicable across qubit platforms and error-correcting codes, clarifying when probabilistic modeling assumptions in quantum hardware design remain justified.\u003c/p\u003e","manuscriptTitle":"When Is a Probabilistic Qubit Model Valid? Subspace Leakage as a Quantitative Diagnostic for Quantum Architectures","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-16 12:23:12","doi":"10.21203/rs.3.rs-8737431/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewersInvited","content":"","date":"2026-03-12T07:59:55+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-03T00:55:34+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-02-03T00:53:47+00:00","index":"","fulltext":""},{"type":"submitted","content":"Quantum Information Processing","date":"2026-01-30T05:31:11+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"quantum-information-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"qinp","sideBox":"Learn more about [Quantum Information Processing](http://link.springer.com/journal/11128)","snPcode":"11128","submissionUrl":"https://submission.nature.com/new-submission/11128/3","title":"Quantum Information Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"364659f0-fa68-4d03-9e98-572d42adbc51","owner":[],"postedDate":"March 16th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-03-16T12:23:12+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-16 12:23:12","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8737431","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8737431","identity":"rs-8737431","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}