Spectral Born machines: classically trainable quantum generative models for discrete data

Quantum Physics arXiv:2607.06675 (quant-ph) [Submitted on 7 Jul 2026] Title:Spectral Born machines: classically trainable quantum generative models for discrete data Authors:Austin Huang, William Maxwell, Vasilis Belis, Evan Peters, Jason Pye, Soran Jahangiri, Joseph Bowles View a PDF of the paper titled Spectral Born machines: classically trainable quantum generative models for discrete data, by Austin Huang and 6 other authors View PDF HTML (experimental) Abstract:We present \emph{spectral Born machines}, a class of quantum generative models that results from viewing and generalizing the class of IQP Born machines through the lens of group Fourier analysis. These quantum models exploit the quantum Fourier transform to create an inductive bias that make them naturally suited to learning integer-structured data, while remaining classically hard to sample from in general. Similar to IQP Born machines, spectral Born machines can be trained efficiently at scale on classical hardware via a maximum mean discrepancy loss based on graph spectral analysis, which we make available in a new \emph{tcdq} module of the PennyLane software platform. In numerical experiments, we show how the spectral bias of the model leads to significantly reduced parameter counts compared to unstructured approaches, and demonstrate the scalability of the software by training a 190-qubit model with over 1 million parameters to successfully learn a distribution of 93 nucleotide-long ribosomal RNA. Our results suggest that highly over-parameterized spectral Born machines may be immune to overfitting, even in strongly data-scarce regimes. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.06675 [quant-ph] (or arXiv:2607.06675v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.06675 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Joseph Bowles [view email] [v1] Tue, 7 Jul 2026 18:00:17 UTC (1,839 KB) Full-text links: Access Paper: View a PDF of the paper titled Spectral Born machines: classically trainable quantum generative models for discrete data, by Austin Huang and 6 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?)