Empirical Evidence of Quantum Kernel Concentration in Few-Shot Keyword Spotting
Richard Caleb, Jagalingam Pushparaj · IEEE Access · 2026
Quantum kernel methods utilize high-dimensional quantum feature spaces as a theoretically motivated strategy to address data scarcity in supervised classification. However, theoretical analyses predict exponential concentration of quantum kernel similarity values as qubit count increases. This study presents the first statistically controlled empirical evaluation of fixed-feature-map quantum support vector machines (QSVMs) for few-shot keyword spotting. The ZZFeatureMap and PauliFeatureMap circuits (2 to 3 qubits, PCA-compressed MFCC features, ~51% variance retained) were evaluated across 24 configurations and four low-resource regimes (5–30 samples per class) on the Google Speech Commands dataset, using ten independent seeds with Wilcoxon signed-rank tests and Bonferroni correction. Across all configurations and sample sizes, QSVM accuracy remained close to the five-class random baseline (19.3% at 30 samples per class; random baseline 20%), while RBF SVM achieved 38.7% and a compact CNN achieved 65.3%. Direct kernel similarity measurement confirmed severe concentration, where the 3-qubit QSVM produced near-identical same-class and different-class similarity means (both approximately 0.192), with 94.1% overlap. Under matched MFCC+PCA features, all classical kernels outperformed QSVM, including linear SVM (Cliff’s $\delta = -0.98$ , $p = 0.002$ ) and RBF SVM ( $\delta = -0.82$ , $p = 0.002$ , Bonferroni-corrected $\alpha = 0.003$ ), with CNN achieving complete stochastic dominance ( $\delta = -1.00$ ). These results empirically validate quantum kernel concentration in structured acoustic classification within evaluated NISQ constraints, and apply specifically to the fixed-feature-map paradigm, not quantum kernel methods in general. The identified failure modes, namely exponential concentration, geometric misalignment, and limited circuit expressivity, provide concrete directions for future research into trainable quantum feature maps and hybrid quantum-classical architectures.