Fourier Analysis of Parametrized Interactive Quantum Classifiers

Quantum Physics arXiv:2609.17991 (quant-ph) [Submitted on 16 Sep 2026] Title:Fourier Analysis of Parametrized Interactive Quantum Classifiers Authors:Fábio Novaes, Fernando M. de Paula Neto, João V. M. Cardoso View a PDF of the paper titled Fourier Analysis of Parametrized Interactive Quantum Classifiers, by F\'abio Novaes and 1 other authors View PDF HTML (experimental) Abstract:Interactive Quantum Classifiers (IQCs) constitute a family of quantum machine learning models inspired by open quantum systems, in which the interaction between a target qubit and an environment is described by a Hamiltonian. Previous works introduced alternative Hamiltonian parameterizations and showed empirically that they can improve classification performance, but the role of these parameters in the resulting classifier remains poorly understood. In this work, we derive a closed-form expression for the reduced quantum channel generated by a parametrized IQC with a single target qubit. The analytical solution explicitly reveals how the Hamiltonian parameters control the constant, sine, and cosine components of the classifier output, establishing a Fourier interpretation of the induced feature map. This analysis motivates a generalized family of Hamiltonian encodings, including matrix-parameterized environmental Hamiltonians whose Fourier components depend on linear combinations of input features, thereby enabling non-separable Fourier structures. Numerical experiments on synthetic and real-world datasets show that the proposed models can improve classification performance on several nonlinear benchmarks. The generalized matrix encoding achieves the strongest aggregate performance in the evaluated benchmark, while a simpler four-parameter extension often attains comparable performance with substantially fewer trainable parameters. We additionally characterize the generated state ensembles using the standard fidelity-based expressibility measure, finding that global expressibility does not directly predict classification performance. Our results provide an analytical characterization of parametrized Hamiltonians in Interactive Quantum Classifiers and establish Fourier analysis as a useful framework for understanding and designing open-system-inspired quantum learning models. Comments: Subjects: Quantum Physics (quant-ph); Machine Learning (cs.LG) Cite as: arXiv:2609.17991 [quant-ph] (or arXiv:2609.17991v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.17991 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Fabio Novaes [view email] [v1] Wed, 16 Sep 2026 01:23:01 UTC (1,337 KB) Full-text links: Access Paper: View a PDF of the paper titled Fourier Analysis of Parametrized Interactive Quantum Classifiers, by F\'abio Novaes and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: cs cs.LG References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)