Hamiltonian-based qutrit quantum neural network with multi-subspace feature map

Hamiltonian-based qutrit quantum neural network with multi-subspace feature map | 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 Hamiltonian-based qutrit quantum neural network with multi-subspace feature map Piero Araujo Rodríguez This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8332601/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract We present QNN-3L, a quantum neural network architecture based on three-level systems (qutrits) with longitudinal Ising-type couplings on a one-dimensional lattice. Starting from an explicit phenomenological multilevel Hamiltonian that includes local anharmonicity, diagonal couplings and resonant control pulses, we derive native selective rotations on computational subspaces and a nearest-neighbour controlled-\((Z)\) primitive. We prove that these native operations generate a subgroup dense in \((\mathrm{SU}(3^N))\), providing approximate universality. To introduce effective nonlinearity while preserving coherent unitary propagation, we propose a hybrid architecture that uses a multi-subspace feature map: classical inputs are encoded via sequential rotations on two independent qutrit subspaces, whose non-commutativity enriches the implicit quantum kernel. We perform ablation studies and kernel diagnostics showing that the multi-subspace encoding yields improved kernel separation and more stable training than single-subspace alternatives. Numerical benchmarks for \((N=3)\)–6 qutrits (dimension \((\dim\mathcal{H}\leq729)\)) demonstrate comparable expressibility at depths \((L\ge3)\) and enhanced shallow-circuit entangling power relative to equivalent qubit circuits, and validate proof-of-concept supervised learning on a canonical nonlinear task. MSC Classification: 03.67.Ac , 03.67.Lx , 07.05.Mh qutrit quantum neural networks feature map non-commutativity quantum machine learning Full Text Additional Declarations No competing interests reported. Supplementary Files supplementarycode.zip Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 20 Apr, 2026 Reviewers agreed at journal 27 Mar, 2026 Reviewers agreed at journal 27 Mar, 2026 Reviewers agreed at journal 27 Mar, 2026 Reviewers invited by journal 27 Mar, 2026 Editor assigned by journal 19 Feb, 2026 Submission checks completed at journal 11 Dec, 2025 First submitted to journal 10 Dec, 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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Starting from an explicit phenomenological multilevel Hamiltonian that includes local anharmonicity, diagonal couplings and resonant control pulses, we derive native selective rotations on computational subspaces and a nearest-neighbour controlled-\\((Z)\\) primitive. We prove that these native operations generate a subgroup dense in \\((\\mathrm{SU}(3^N))\\), providing approximate universality. To introduce effective nonlinearity while preserving coherent unitary propagation, we propose a hybrid architecture that uses a multi-subspace feature map: classical inputs are encoded via sequential rotations on two independent qutrit subspaces, whose non-commutativity enriches the implicit quantum kernel. We perform ablation studies and kernel diagnostics showing that the multi-subspace encoding yields improved kernel separation and more stable training than single-subspace alternatives. Numerical benchmarks for \\((N=3)\\)–6 qutrits (dimension \\((\\dim\\mathcal{H}\\leq729)\\)) demonstrate comparable expressibility at depths \\((L\\ge3)\\) and enhanced shallow-circuit entangling power relative to equivalent qubit circuits, and validate proof-of-concept supervised learning on a canonical nonlinear task.\u003c/p\u003e\n\u003cp\u003eMSC Classification: 03.67.Ac , 03.67.Lx , 07.05.Mh\u003c/p\u003e","manuscriptTitle":"Hamiltonian-based qutrit quantum neural network with multi-subspace feature map","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-05 08:56:12","doi":"10.21203/rs.3.rs-8332601/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-04-20T10:59:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"182444062446978420838242661166787423011","date":"2026-03-27T13:21:50+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"259725900788463026467380677460396788515","date":"2026-03-27T12:30:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"53251613345276420900051161615612904766","date":"2026-03-27T12:26:49+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-27T12:21:50+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-19T13:16:56+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-11T05:57:01+00:00","index":"","fulltext":""},{"type":"submitted","content":"Quantum Machine Intelligence","date":"2025-12-11T04:51:37+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"quantum-machine-intelligence","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"qumi","sideBox":"Learn more about [Quantum Machine Intelligence](http://link.springer.com/journal/42484)","snPcode":"42484","submissionUrl":"https://submission.nature.com/new-submission/42484/3","title":"Quantum Machine Intelligence","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"e7d1307f-a147-467f-ba0f-31ca26a318f8","owner":[],"postedDate":"February 5th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-03-27T13:07:31+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-05 08:56:12","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8332601","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8332601","identity":"rs-8332601","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}