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.