Spectral Phase Encoding for Quantum Kernel Methods

TL;DR

This paper introduces Spectral Phase Encoding (SPE), a hybrid quantum feature construction method that enhances robustness of quantum kernel methods against data noise, outperforming other variants and classical baselines in stability.

Contribution

The paper proposes Spectral Phase Encoding (SPE), combining DFT with phase-only embedding, and demonstrates its superior robustness to noise compared to other quantum and classical methods.

Findings

DFT-based preprocessing yields minimal degradation under noise.

QK-DFT shows comparable or better stability than classical SVMs.

Hardware experiments confirm SPE's stability and executability.

Abstract

Quantum kernel methods are promising for near-term quantum ma- chine learning, yet their behavior under data corruption remains insuf- ficiently understood. We analyze how quantum feature constructions degrade under controlled additive noise. We introduce Spectral Phase Encoding (SPE), a hybrid construc- tion combining a discrete Fourier transform (DFT) front-end with a diagonal phase-only embedding aligned with the geometry of diagonal quantum maps. Within a unified framework, we compare QK-DFT against alternative quantum variants (QK-PCA, QK-RP) and classi- cal SVM baselines under identical clean-data hyperparameter selection, quantifying robustness via dataset fixed-effects regression with wild cluster bootstrap inference across heterogeneous real-world datasets. Across the quantum family, DFT-based preprocessing yields the smallest degradation rate as noise increases, with statistically sup- ported slope differences relative to PCA and RP. Compared to classical baselines, QK-DFT shows degradation comparable to linear SVM and more stable than RBF SVM under matched tuning. Hardware exper- iments confirm that SPE remains executable and numerically stable for overlap estimation. These results indicate that robustness in quan- tum kernels depends critically on structure-aligned preprocessing and its interaction with diagonal embeddings, supporting a robustness-first perspective for NISQ-era quantum machine learning.