Spectral phase encoding for quantum kernel methods

Abstract Quantum kernel methods are promising for near-term quantum machine learning, yet their behavior under data corruption remains insufficiently understood. We analyze how quantum feature constructions degrade under controlled additive noise. We introduce Spectral Phase Encoding (SPE), a hybrid construction combining a discrete Fourier transform (DFT) front-end with a diagonal phase-only embedding. Within a unified framework, we compare the resulting DFT-based quantum-kernel pipeline () against alternative quantum variants based on principal component analysis (PCA) and random projections (RP), as well as classical support vector machine (SVM) baselines, under identical clean-data hyperparameter selection. Robustness is quantified via dataset fixed-effects regression with wild cluster bootstrap inference across heterogeneous real-world datasets. Across the matched quantum family, DFT-based preprocessing yields the smallest degradation rate as noise increases, with statistically supported slope differences relative to PCA and RP. Compared with classical baselines, shows degradation comparable to linear SVM and more favorable than radial basis function (RBF) SVM under the present tuning protocol. Hardware experiments further confirm that the resulting overlap-estimation primitive remains executable and numerically stable. Taken together, these results support a robustness-first view of quantum kernel evaluation and show that, within the controlled pipeline family studied here, structure-aligned spectral preprocessing combined with a shared diagonal quantum embedding can yield slower degradation under corruption.