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

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 recently developed data augmentation technique from quantum harmonic analysis and implements 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.

arXiv:2604.18691 [quant-ph]

(or arXiv:2604.18691v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2604.18691 Focus to learn more arXiv-issued DOI via DataCite

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