Simulation-Based Explainable AI for Quantum Dynamics: Neural Proxies and SHAP for Entanglement Analysis

Simulation-Based Explainable AI for Quantum Dynamics: Neural Proxies and SHAP for Entanglement Analysis | 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 Simulation-Based Explainable AI for Quantum Dynamics: Neural Proxies and SHAP for Entanglement Analysis Muhammad Shaharyar Nasir This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8584766/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 The challenge of quantum measurement, wherein observation collapses the wavefunction, hinders non-invasive study of phenomena such as entanglement and superposition. This is especially problematic when analyzing the temporal evolution of multi-qubit systems, where repeated measurement disrupts the very dynamics under investigation. Inspired by challenges in interpreting black-box machine learning models, we propose a simulation-to-explainable AI (XAI) framework for analyzing entanglement dynamics through neural network proxies and interpretability analysis. Using QuTiP-based simulations, we generate temporal correlation data from entangled two-, four-, and six-qubit systems evolving under structured Hamiltonians~\cite{johansson2013}. Classical neural networks trained on this data achieve high accuracy in reproducing entanglement metrics, with mean squared errors of 0.0196 (2 qubits), 0.025 (4 qubits), and 0.0361 (6 qubits). Applying SHAP (SHapley Additive exPlanations)~\cite{lundberg2017}, we uniquely identify temporal features ($t \approx 2.5$ and $7.5$) that reveal entanglement oscillation phases, enhancing interpretability beyond traditional simulation endpoints. We propose a framework integrating neural-network proxies with explainable AI techniques to analyze quantum dynamics. Importantly, our approach is strictly \emph{collapse-free within classical simulations}: it does not address the measurement problem in quantum foundations but avoids explicit projective measurement in the numerical pipeline. The method combines QuTiP-based simulations, neural approximations of unitary dynamics, and SHAP-based interpretability applied to temporal entanglement features. As of September 2025, this work supports NISQ-era applications with freely accessible code and data at Zenodo (DOI: \href{ https://doi.org/10.5281/zenodo.17216687}{10.5281/zenodo.17216687} ). Physical sciences/Mathematics and computing Physical sciences/Physics 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. 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-8584766","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":600234734,"identity":"9039ebeb-630e-45eb-bef9-4a54ec8e8dd5","order_by":0,"name":"Muhammad Shaharyar Nasir","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEklEQVRIiWNgGAWjYHACNgbGBjhHgoEfRCUUkKJFEsRJMCBeCwODwQEwiVu9bgP7swc/d9jlGxw/++zBjz8W+cbnVyd+eGDAIM8vdgCrFrMDPOaGvWeSLTecSQcy2iQst914u1kC6DDDmbMTcGlhk+BtYzYwOJAGZDRIGJjdOLsBpCXB4DYuLezPJP+21RsYnH/GJvnnj4SB8Yyzm3/g18JgJs3bdtjA4EYamzTQRgMD/t5t+G05zGMmLdt23EDyxjM2IEPCQOIG7zaLBAMJ3H453v5M8m1btQHf+TQ2yTd/6gz4+89uvvmjwkaeXxq7FgZmKK1wACYiAVYpgV05MpBvgLH4D+BWNQpGwSgYBSMSAAAaP1x/T+Y1NwAAAABJRU5ErkJggg==","orcid":"","institution":"Independent Researcher","correspondingAuthor":true,"prefix":"","firstName":"Muhammad","middleName":"Shaharyar","lastName":"Nasir","suffix":""}],"badges":[],"createdAt":"2026-01-12 18:53:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8584766/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8584766/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109240887,"identity":"7c14a9e1-6155-42e2-81cf-b4a01452eb0b","added_by":"auto","created_at":"2026-05-14 06:41:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1895513,"visible":true,"origin":"","legend":"","description":"","filename":"SimulationBasedExplainableAIforQuantumDynamicspeerreview3.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8584766/v1_covered_c35e2e42-6faf-4107-a99d-b600ccbfb06d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Simulation-Based Explainable AI for Quantum Dynamics: Neural Proxies and SHAP for Entanglement Analysis","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-8584766/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8584766/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The challenge of quantum measurement, wherein observation collapses the wavefunction, hinders non-invasive study of phenomena such as entanglement and superposition. This is especially problematic when analyzing the temporal evolution of multi-qubit systems, where repeated measurement disrupts the very dynamics under investigation. Inspired by challenges in interpreting black-box machine learning models, we propose a simulation-to-explainable AI (XAI) framework for analyzing entanglement dynamics through neural network proxies and interpretability analysis.\nUsing QuTiP-based simulations, we generate temporal correlation data from entangled two-, four-, and six-qubit systems evolving under structured Hamiltonians~\\cite{johansson2013}. Classical neural networks trained on this data achieve high accuracy in reproducing entanglement metrics, with mean squared errors of 0.0196 (2 qubits), 0.025 (4 qubits), and 0.0361 (6 qubits). 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