Quantum-computing within a bosonic context: Assessing finite basis effects on prototypical vibrational Hamiltonian spectra

Quantum-computing within a bosonic context: Assessing finite basis effects on prototypical vibrational Hamiltonian spectra | 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 Quantum-computing within a bosonic context: Assessing finite basis effects on prototypical vibrational Hamiltonian spectra Joachim Knapik, Bruno Senjean, Benjamin Lasorne, Yohann Scribano This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7490195/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Dec, 2025 Read the published version in Theoretical Chemistry Accounts → Version 1 posted 9 You are reading this latest preprint version Abstract Quantum computing has recently been emerging in theoretical chemistry as a realistic avenue meant to offer computational speedup to challenging eigenproblems in the context of strongly-correlated molecular systems or extended materials. Most studies so far have been devoted to the quantum treatment of electronic structure, for which the transformation of fermionic operators into the qubit space is quite transparent. In contrast, only a few were directed to the quantum treatment of vibrational structure, which at the moment remains not devoid of unknowns. When simulating an anharmonic vibrational mode under bosonic second quantization, the biggest problem, which we analyze in detail in the present work, is the disruption of the resolution of the identity when truncating the infinite harmonic-oscillator basis set of primitive modals and how this alters the canonical commutation relation. This may lead to serious incorrectness in the evaluation of the Hamiltonian matrix elements when assembling them from finite matrix products, which eventually entail a nonvariational behavior with respect to the finite size of the computational basis. As we show here, a simple cure occurs to be obtained upon using Wick's normal order, for reasons that are not standardly evoked. We also provide a detailed comparison between the boson-to-qubit unary and binary mappings under two different representations: one for the bosonic ladder operators within the harmonic-oscillator primitive basis, and one for the so-called n-mode representation within any type of computational basis. In addition, we discuss the impact of choosing an adequate primitive basis set in terms of quantum computing with respect to its variational convergence efficiency (number of basis functions, hence of qubits) and as regards the magnitude of the 1-norm of the encoded Hamiltonian (a measure of the computational complexity of the quantum algorithm). Such fundamental aspects are illustrated numerically on a one-dimensional anharmonic Hamiltonian model corresponding to a symmetric double-well potential, of interest both for vibrational spectroscopy and chemical reactivity, and which is a challenging situation for numerical convergence due to fine tunneling splitting. quantum computing Hamiltonian mapping qubit encoding ladder operators and normal order bosonic modes vibrational structure tunneling in spectroscopy and chemistry Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 20 Dec, 2025 Read the published version in Theoretical Chemistry Accounts → Version 1 posted Editorial decision: Revision requested 04 Nov, 2025 Reviews received at journal 04 Nov, 2025 Reviews received at journal 17 Oct, 2025 Reviewers agreed at journal 14 Oct, 2025 Reviewers agreed at journal 13 Oct, 2025 Reviewers invited by journal 08 Sep, 2025 Editor assigned by journal 07 Sep, 2025 Submission checks completed at journal 06 Sep, 2025 First submitted to journal 29 Aug, 2025 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-7490195","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":513625921,"identity":"d0446791-9f6d-4ed4-b5e0-dfff8ffaf768","order_by":0,"name":"Joachim Knapik","email":"","orcid":"","institution":"University of Montpellier","correspondingAuthor":false,"prefix":"","firstName":"Joachim","middleName":"","lastName":"Knapik","suffix":""},{"id":513625923,"identity":"2d89a9d7-586e-42ed-a4f2-2c3335313f4f","order_by":1,"name":"Bruno Senjean","email":"","orcid":"","institution":"University of Montpellier","correspondingAuthor":false,"prefix":"","firstName":"Bruno","middleName":"","lastName":"Senjean","suffix":""},{"id":513625924,"identity":"dbdb54bd-42a7-4d00-bee1-291844550411","order_by":2,"name":"Benjamin Lasorne","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABRklEQVRIie3Rv2qDUBQG8BMueJfbZlVCzSscuWAa6MPo0qWmfyiUTI0loEtCV1+jCE4dLriGzg6BtghODRiyNNBCbzXpoHYv1A9E7qc/zhEB2rT5g8HyUgHorunuHx3Sjitv+u+E7Brt+z2wABRSEN5EyuwJih9SnGtkQOficuscnwMhab5+XOo8ObPTq/elrhByl44BLypkOHuyjHmkXgNRTC3IMm4mo5AHVsblYlNjATh0K4slDuJBpNouAZMwEdtRMop6zIptj3Q8+WEfWJmCz29ofBaEbjaSTMKgJBNJ/K0LWCMJQ15OYdiTxEK1JJZczOs0kOHMQX4kiUfYjRaI2AgWq5Cz08yQU6aaizUyoAvTWEW39j31wzwXcb/rjx5SdrLsd6n/unbHNSKjFJ1SacV+8zqQ//ClqRVNZZs2bdr8z3wBEKJrNLOUJHEAAAAASUVORK5CYII=","orcid":"","institution":"University of Montpellier","correspondingAuthor":true,"prefix":"","firstName":"Benjamin","middleName":"","lastName":"Lasorne","suffix":""},{"id":513625925,"identity":"c04b8582-c12f-4e08-b172-cc542a7fc515","order_by":3,"name":"Yohann Scribano","email":"","orcid":"","institution":"University of Montpellier","correspondingAuthor":false,"prefix":"","firstName":"Yohann","middleName":"","lastName":"Scribano","suffix":""}],"badges":[],"createdAt":"2025-08-29 16:08:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7490195/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7490195/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00214-025-03269-3","type":"published","date":"2025-12-20T15:57:33+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":98813910,"identity":"abb49aa6-f3c2-4ab7-8855-e30db4faa01b","added_by":"auto","created_at":"2025-12-22 16:07:35","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":569283,"visible":true,"origin":"","legend":"","description":"","filename":"manuscriptlasornetca.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7490195/v1_covered_181e5e1a-cba3-45a5-803a-83e593114652.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Quantum-computing within a bosonic context: Assessing finite basis effects on prototypical vibrational Hamiltonian spectra","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"theoretical-chemistry-accounts","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"tcac","sideBox":"Learn more about [Theoretical Chemistry Accounts](http://link.springer.com/journal/214)","snPcode":"214","submissionUrl":"https://submission.nature.com/new-submission/214/3","title":"Theoretical Chemistry Accounts","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"quantum computing, Hamiltonian mapping, qubit encoding, ladder operators and normal order, bosonic modes, vibrational structure, tunneling in spectroscopy and chemistry","lastPublishedDoi":"10.21203/rs.3.rs-7490195/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7490195/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Quantum computing has recently been emerging in theoretical chemistry as a realistic avenue meant to offer computational speedup to challenging eigenproblems in the context of strongly-correlated molecular systems or extended materials. 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