Harmoniq: Efficient Data Augmentation on a Quantum Computer Inspired by Harmonic Analysis
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Quantum Physics arXiv:2604.18691 (quant-ph) [Submitted on 20 Apr 2026] Title:Harmoniq: Efficient Data Augmentation on a Quantum Computer Inspired by Harmonic Analysis Authors:Kristina Kirova, Monika Doerfler, Franz Luef, Richard Kueng View a PDF of the paper titled Harmoniq: Efficient Data Augmentation on a Quantum Computer Inspired by Harmonic Analysis, by Kristina Kirova and 3 other authors View PDF HTML (experimental) Abstract:Quantum machine learning has attracted significant interest in recent years. Most existing approaches, however, are variational in nature and require extensive parameter optimization subroutines. Here, we propose a conceptually distinct quantum machine learning approach that goes beyond the variational paradigm. Harmoniq takes a novel data augmentation technique from quantum harmonic analysis and approximates it as a stochastic mixture of n-qubit circuits with (at most) quadratic depth each. A key strength of Harmoniq is its modularity: viewed as a quantum process acting on density matrices, it can readily be combined with other quantum data processing and learning subroutines. A subsequent case study demonstrates this modularity by combining Harmoniq with stochastic amplitude encoding for the input density matrix and quantum PCA on the output density matrix. This results in a promising signal denoising pipeline that works particularly well in the small sample size regime. Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2604.18691 [quant-ph] (or arXiv:2604.18691v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.18691 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Kristina Kirova [view email] [v1] Mon, 20 Apr 2026 18:00:04 UTC (4,062 KB) Full-text links: Access Paper: View a PDF of the paper titled Harmoniq: Efficient Data Augmentation on a Quantum Computer Inspired by Harmonic Analysis, by Kristina Kirova and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: math math-ph math.MP 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?)