Quantum Fourier Generative Models Trainable at Large Scale

Quantum Physics arXiv:2606.28483 (quant-ph) [Submitted on 26 Jun 2026] Title:Quantum Fourier Generative Models Trainable at Large Scale Authors:Cenk Tüysüz, Oleksandr Kyriienko, Michele Grossi View a PDF of the paper titled Quantum Fourier Generative Models Trainable at Large Scale, by Cenk T\"uys\"uz and 2 other authors View PDF Abstract:We propose an algorithmic framework for building and training quantum generative models corresponding to multivariate probability distributions. Our model uses parallel Fourier feature maps for embedding continuous-valued variables combined with a forrelation-type quantum circuit for tuning Fourier coefficients of the quantum model. Crucially, we develop a distinct training strategy where training is enabled at large scale by log-likelihood loss with unbiased Monte Carlo estimator based on Parseval's identity. Unlike prior work that relied on maximal mean discrepancy (MMD) loss, our approach goes beyond matching just low frequency moments, while enabling efficient classical training. Once the model is trained, we use inverse quantum Fourier transforms to map it into a separate sampling circuit in the computational basis. We demonstrate the efficiency of the suggested framework by validating loss estimation at the scale of over 1000 qubits on a single GPU. We show that univariate and bivariate models with highly non-trivial structure can be trained to low total variation distance, while fine-tuned IQP models with MMD loss show poor performance. Comparing to classical baselines represented by normalizing flow and diffusion models, we show that our approach avoids oversmoothing and preserves multi-modal structure of the target. Finally, we have deployed the trained models on superconducting quantum devices, successfully sampling distributions with per-sample execution times of approximately $300\,\mu\mathrm{s}$. Our work shows that quantum generative models with the train-on-classical deploy-on-quantum approach can provide both high-quality structure at increased scale and fast sampling access needed for inference. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.28483 [quant-ph] (or arXiv:2606.28483v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.28483 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Cenk Tüysüz [view email] [v1] Fri, 26 Jun 2026 18:00:00 UTC (8,417 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Fourier Generative Models Trainable at Large Scale, by Cenk T\"uys\"uz and 2 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)