Mathematical Beauty as Computational Advantage: Exceptional Lie Groups in Quantum Reservoir Computing

Mathematical Beauty as Computational Advantage: Exceptional Lie Groups in Quantum Reservoir Computing | 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 Physical Sciences - Article Mathematical Beauty as Computational Advantage: Exceptional Lie Groups in Quantum Reservoir Computing Justin Howard-Stanley This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8355784/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 demonstrate that exceptional Lie groups (E6, E7, E8, F4, G2) provide genuine computational advantages over classical Lie groups (A, B, C, D series) in quantum reservoir computing. Through systematic experiments on the qBraid IonQ simulator, we show that E6 achieves 58.0% higher information entropy than classical structures (Cohen’s d = 1.884), with participation ratio strongly correlating with performance (r = 0.963, p < 0.01). The exceptional advantage stems from superior quantum state utilization: E6 shows 115.9% higher participation ratio than classical average. These results provide empirical evidence that mathematical elegance translates directly to computational power, suggesting that nature’s most beautiful mathematical structures may be optimal substrates for quantum information processing. Physical sciences/Physics/Quantum physics/Quantum information Physical sciences/Physics/Quantum physics/Quantum simulation Exceptional Lie groups Quantum reservoir computing E8 lattice Quantum state utilization Mathematical beauty Full Text Additional Declarations Yes there is potential Competing Interest. I accidently submitted this to scientific reports and don't know if that should be listed here. 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-8355784","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":560545573,"identity":"09dfb0c9-636d-4f00-8c55-53426304efb0","order_by":0,"name":"Justin Howard-Stanley","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6klEQVRIiWNgGAWjYBAC+RlAgrGBQYaPgYfxAZDNw0dIi8ENiBYeNgYeZgOQFjaCWiQQWthAbAbCWqSbj278ucOOh4397LHKrzl2MmwMzA8f3cDnlznH0m7znknmYePJS7stuw3IYGAzNs7BZ82NHLPbjG3MQJVAhuQ2ZrALpfFryf9282dbPQ8b/xuzYslt9cRoyWG7wdt2GOj3HDPGj9sOE9ZicCPN7DZv23GgljfG0ozbgAxmAn6Rn5H8DOiwajl+/hzDjz+3Vdvzszc/fIzXYciAmQdMEqscBBh/kKJ6FIyCUTAKRgwAAMiOQo0r70l8AAAAAElFTkSuQmCC","orcid":"","institution":"Independent researcher","correspondingAuthor":true,"prefix":"","firstName":"Justin","middleName":"","lastName":"Howard-Stanley","suffix":""}],"badges":[],"createdAt":"2025-12-14 04:05:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8355784/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8355784/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102182388,"identity":"9d70d170-e418-4eec-ab69-489cc1fe0924","added_by":"auto","created_at":"2026-02-09 07:33:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":238426,"visible":true,"origin":"","legend":"Article File","description":"","filename":"Beautifulmathematicians.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8355784/v1_covered_e135f89f-b792-41a8-b49f-69516d837dc8.pdf"}],"financialInterests":"\u003cb\u003eYes\u003c/b\u003e there is potential Competing Interest.\nI accidently submitted this to scientific reports and don't know if that should be listed here.","formattedTitle":"Mathematical Beauty as Computational Advantage:\nExceptional Lie Groups in Quantum Reservoir\nComputing","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":"Exceptional Lie groups, Quantum reservoir computing, E8 lattice, Quantum state utilization, Mathematical beauty","lastPublishedDoi":"10.21203/rs.3.rs-8355784/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8355784/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We demonstrate that exceptional Lie groups (E6, E7, E8, F4, G2) provide genuine\r\ncomputational advantages over classical Lie groups (A, B, C, D series) in quantum reservoir\r\ncomputing. Through systematic experiments on the qBraid IonQ simulator, we show that\r\nE6 achieves 58.0% higher information entropy than classical structures (Cohen’s d = 1.884),\r\nwith participation ratio strongly correlating with performance (r = 0.963, p \u003c 0.01). The\r\nexceptional advantage stems from superior quantum state utilization: E6 shows 115.9%\r\nhigher participation ratio than classical average. These results provide empirical evidence\r\nthat mathematical elegance translates directly to computational power, suggesting that\r\nnature’s most beautiful mathematical structures may be optimal substrates for quantum\r\ninformation processing.","manuscriptTitle":"Mathematical Beauty as Computational Advantage:\nExceptional Lie Groups in Quantum Reservoir\nComputing","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-09 07:33:53","doi":"10.21203/rs.3.rs-8355784/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":"de9ce09a-29d5-41ee-adff-375dd1b46928","owner":[],"postedDate":"February 9th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":59671620,"name":"Physical sciences/Physics/Quantum physics/Quantum information"},{"id":59671621,"name":"Physical sciences/Physics/Quantum physics/Quantum simulation"}],"tags":[],"updatedAt":"2026-02-09T07:33:53+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-09 07:33:53","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8355784","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8355784","identity":"rs-8355784","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}