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Harmoniq: Efficient Data Augmentation on a Quantum Computer Inspired by Harmonic Analysis

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arXiv:2604.18691v1 Announce Type: new 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 c

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Quantum Physics [Submitted on 20 Apr 2026] Harmoniq: Efficient Data Augmentation on a Quantum Computer Inspired by Harmonic Analysis Kristina Kirova, Monika Doerfler, Franz Luef, Richard Kueng 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 Submission history From: Kristina Kirova [view email] [v1] Mon, 20 Apr 2026 18:00:04 UTC (4,062 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev | next > new | recent | 2026-04 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

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