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.
@article{arxiv.2604.18691,
title = {Harmoniq: Efficient Data Augmentation on a Quantum Computer Inspired by Harmonic Analysis},
author = {Kristina Kirova and Monika Doerfler and Franz Luef and Richard Kueng},
journal= {arXiv preprint arXiv:2604.18691},
year = {2026}
}