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

TL;DR

Harmoniq introduces a novel, modular quantum data augmentation method inspired by harmonic analysis, enabling improved quantum machine learning pipelines without variational optimization.

Contribution

It presents a new quantum data augmentation technique that is modular, efficient, and can be integrated with existing quantum algorithms, moving beyond variational methods.

Findings

Effective in small sample size regimes

Combines well with quantum PCA and amplitude encoding

Enhances quantum machine learning pipelines

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.