Benchmarking Encoding Families in Quantum Neural Networks Under Fixed Circuit Area for Frequency Spectrum and Trainability

Benchmarking Encoding Families in Quantum Neural Networks Under Fixed Circuit Area for Frequency Spectrum and Trainability | 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 Benchmarking Encoding Families in Quantum Neural Networks Under Fixed Circuit Area for Frequency Spectrum and Trainability Martyna Czuba, Patrick Holzer, Hein Zay Yar Oo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9115478/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Quantum Neural Networks (QNNs) offer a promising framework for integrating quantum computing principles into machine learning, yet their practical capabilities and limitations remain insufficiently studied. In this work, we systematically investigate the trainability and approximation properties of QNNs by benchmarking diverse circuit architectures and encoding strategies across synthetic and real-world datasets.We analyze several ansätze, including Hamming, binary, exponential, ternary, turnpike and Golomb, by evaluating their ability to learn synthetic data modeled as random finite Fourier series. To assess real-world applicability, we further evaluate QNNs on two time-series classification tasks: a Fischertechnik pneumatic leak detection dataset and the publicly available NASA bearing fault dataset.Our experiments show that while broader frequency spectra can theoretically enhance expressivity, practical trainability is strongly influenced by architectural factors such as qubit count and circuit depth. Notably, we find that QNNs perform best when the frequency spectrum is tailored to the target function’s complexity but remains as compact as possible. Moreover, architectures with identical frequency spectra can differ in trainability, with configurations using more qubits and fewer layers generally performing better, except in the single-layer case.These findings provide guidelines for selecting QNN ansätze and offer new insights into the interplay between expressivity and trainability in quantum machine learning. variational quantum-machine-learning parametrized quantum circuits data encoding Fourier series Benchmarking Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 13 Apr, 2026 Reviewers invited by journal 08 Apr, 2026 Editor assigned by journal 15 Mar, 2026 Submission checks completed at journal 14 Mar, 2026 First submitted to journal 13 Mar, 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-9115478","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":606265913,"identity":"32dc8769-31e3-4bd6-82eb-bd4ac2973848","order_by":0,"name":"Martyna Czuba","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAklEQVRIiWNgGAWjYJADNgaGCghLAohl8KhkbEBoOcPAwAPVwkOcFsY2IrTotp99/ph3hx0Df/8Zswc/5x2Wt2dgPnibh+EOTi1mZ9INm3nPJDNIHDhjbti77bBhDwNbsjUPwzPcWg6kMTbztjEzGDD2mEnwbrvN2MPAYybNw3AYt5bzz0Ba6hkMmHnMJP/OuW3fw8D/Db+WG2BbDjMYsAEN5224nQi0hY2AlmeMM+e2HeeROMNWbixz7H9yz2E2Y8s5Bnj8cj6N4cPbtmo5/v7D2x6+qUmzbW9vfnjjTcUdOVxaQICJByUWmEGEwQF8OhgYf2ARxK9lFIyCUTAKRhQAAE9ATnXGpL5DAAAAAElFTkSuQmCC","orcid":"","institution":"Military University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Martyna","middleName":"","lastName":"Czuba","suffix":""},{"id":606265914,"identity":"833ace20-f6cb-4327-997c-1da90026bd34","order_by":1,"name":"Patrick Holzer","email":"","orcid":"","institution":"Fraunhofer Institute for Industrial Mathematics ITWM","correspondingAuthor":false,"prefix":"","firstName":"Patrick","middleName":"","lastName":"Holzer","suffix":""},{"id":606265915,"identity":"1dc00203-ed26-4749-870d-4f8ca3ed1c72","order_by":2,"name":"Hein Zay Yar Oo","email":"","orcid":"","institution":"Georgia Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Hein","middleName":"Zay Yar","lastName":"Oo","suffix":""}],"badges":[],"createdAt":"2026-03-13 13:54:43","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9115478/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9115478/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105967200,"identity":"9747a221-df55-48f6-a024-107722ff681a","added_by":"auto","created_at":"2026-04-02 02:25:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1403275,"visible":true,"origin":"","legend":"","description":"","filename":"CzubaQNNFrequencySpectrumsubmission.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9115478/v1_covered_7c4dcaf5-8cd8-4c52-8ca4-6c0e01d9541e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Benchmarking Encoding Families in Quantum Neural Networks Under Fixed Circuit Area for Frequency Spectrum and Trainability","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"variational quantum-machine-learning, parametrized quantum circuits, data encoding, Fourier series, Benchmarking","lastPublishedDoi":"10.21203/rs.3.rs-9115478/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9115478/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e Quantum Neural Networks (QNNs) offer a promising framework for integrating quantum computing principles into machine learning, yet their practical capabilities and limitations remain insufficiently studied. In this work, we systematically investigate the trainability and approximation properties of QNNs by benchmarking diverse circuit architectures and encoding strategies across synthetic and real-world datasets.We analyze several ans\u0026auml;tze, including Hamming, binary, exponential, ternary, turnpike and Golomb, by evaluating their ability to learn synthetic data modeled as random finite Fourier series. To assess real-world applicability, we further evaluate QNNs on two time-series classification tasks: a Fischertechnik pneumatic leak detection dataset and the publicly available NASA bearing fault dataset.Our experiments show that while broader frequency spectra can theoretically enhance expressivity, practical trainability is strongly influenced by architectural factors such as qubit count and circuit depth. Notably, we find that QNNs perform best when the frequency spectrum is tailored to the target function\u0026rsquo;s complexity but remains as compact as possible. Moreover, architectures with identical frequency spectra can differ in trainability, with configurations using more qubits and fewer layers generally performing better, except in the single-layer case.These findings provide guidelines for selecting QNN ans\u0026auml;tze and offer new insights into the interplay between expressivity and trainability in quantum machine learning.\u003c/p\u003e","manuscriptTitle":"Benchmarking Encoding Families in Quantum Neural Networks Under Fixed Circuit Area for Frequency Spectrum and Trainability","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-02 02:24:10","doi":"10.21203/rs.3.rs-9115478/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"18052238984040137975221809391293752678","date":"2026-04-13T12:57:47+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-08T11:44:56+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-15T05:59:29+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-14T07:23:52+00:00","index":"","fulltext":""},{"type":"submitted","content":"Quantum Information Processing","date":"2026-03-13T13:48:28+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":"d16354a6-0d3a-455a-af5e-ae2648dec7b6","owner":[],"postedDate":"April 2nd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-08T11:54:09+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-02 02:24:10","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9115478","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9115478","identity":"rs-9115478","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}