Trapped-ion coherence does not decay purely exponentially :- a weak power-law tail is always present, and we quantify it with α ≈ 0.1–0.3

Trapped-ion coherence does not decay purely exponentially :- a weak power-law tail is always present, and we quantify it with α ≈ 0.1–0.3 | 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 Trapped-ion coherence does not decay purely exponentially :- a weak power-law tail is always present, and we quantify it with α ≈ 0.1–0.3 khushboo rani This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8156121/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 This work presents an empirical characterization of long-time coherence decay in a trapped-ion qubit on the IonQ Forte-1 quantum processor using high-depth CPMG dynamical-decoupling sequences. Across 97 independent runs, the measured coherence envelope exhibits a shallow long-time curvature that a standard single-exponential model cannot capture. To summarize the behavior over a wide time range, we introduce an extended empirical envelope of the form C(t) = A exp(−t/τ) t⁻ᵅ , which significantly improves fit quality (AIC/BIC, RMSE, and residual autocorrelation) relative to a pure exponential decay. The extracted power-law exponents fall in the range 0.1 ≤ α ≤ 0.3 , indicating persistent long-time structure in the coherence decay. This extended envelope provides a compact descriptive model for benchmarking trapped-ion systems, evaluating dynamical-decoupling performance, and informing hardware-aware noise characterization. The empirical crossover timescale tₚ = ατ offers a simple indicator of when the power-law component becomes relevant within the experimental window. The methods include AWS Braket execution, IonQ device calibration reporting, nonlinear least-squares fitting, and statistical diagnostics. This dataset and analysis serve as a practical reference for long-time coherence studies in trapped-ion quantum hardware. Quantum Quantum decoherence ion Trapped Qbits 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. 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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-8156121","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":547581193,"identity":"bd01623e-e4ed-4d4f-b697-fa4e05caf8b6","order_by":0,"name":"khushboo rani","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+0lEQVRIiWNgGAWjYBACCQkGBmYGAwYGfvaGBIMPQBE2dmK1SPYceFA4A6SFmSgtQGBwI/HBZx4Qi5AWydk9xp8LCu7JMxxITtxs82ubPB8zA+OHjzm4tUjLnDGTnmFQbNjYcCzZOLfvtmEbMwOz5MxtuLXISeSYMfMYJDA2M/akGef23GYEamFj5sWvxfgzUIt9GzP/99+WPbftCWqRlsgxkAZqSexhY0gwZvhxO5GgFskZaWUgLckzeBgSDHsbbie3MTM24/WLxI3kzZ95/iTY7r//IMHgx5/btvPbmw9++IhHCypgbAOTDcSqB4E/pCgeBaNgFIyCkQIAUThNVe2XDokAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0006-7000-026X","institution":"IIIT Banglore","correspondingAuthor":true,"prefix":"","firstName":"khushboo","middleName":"","lastName":"rani","suffix":""}],"badges":[],"createdAt":"2025-11-19 14:00:59","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-8156121/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8156121/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96372454,"identity":"fca42d89-411e-43e5-b023-dc7c99e41296","added_by":"auto","created_at":"2025-11-20 10:27:43","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":403505,"visible":true,"origin":"","legend":"","description":"","filename":"paperquantdecoherencekhushboo.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8156121/v1_covered_e5cf7daa-027f-45e2-aac4-503b821e8b24.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eTrapped-ion coherence does not decay purely exponentially :- a weak power-law tail is always present, and we quantify it with α ≈ 0.1–0.3\u003c/p\u003e","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, Quantum decoherence , ion Trapped Qbits","lastPublishedDoi":"10.21203/rs.3.rs-8156121/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8156121/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis work presents an empirical characterization of long-time coherence decay in a trapped-ion qubit on the IonQ Forte-1 quantum processor using high-depth CPMG dynamical-decoupling sequences. Across 97 independent runs, the measured coherence envelope exhibits a shallow long-time curvature that a standard single-exponential model cannot capture.\u003c/p\u003e\n\u003cp\u003eTo summarize the behavior over a wide time range, we introduce an extended empirical envelope of the form\u003cbr\u003e\n\u003cstrong\u003eC(t) = A exp(−t/τ) t⁻ᵅ\u003c/strong\u003e,\u003cbr\u003e\nwhich significantly improves fit quality (AIC/BIC, RMSE, and residual autocorrelation) relative to a pure exponential decay. The extracted power-law exponents fall in the range \u003cstrong\u003e0.1 ≤ α ≤ 0.3\u003c/strong\u003e, indicating persistent long-time structure in the coherence decay.\u003c/p\u003e\n\u003cp\u003eThis extended envelope provides a compact descriptive model for benchmarking trapped-ion systems, evaluating dynamical-decoupling performance, and informing hardware-aware noise characterization. The empirical crossover timescale \u003cstrong\u003etₚ = ατ\u003c/strong\u003e offers a simple indicator of when the power-law component becomes relevant within the experimental window.\u003c/p\u003e\n\u003cp\u003eThe methods include AWS Braket execution, IonQ device calibration reporting, nonlinear least-squares fitting, and statistical diagnostics. 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