Quantum Kernel Concentration Under Class Imbalance: Empirical Characterisation with Discrimination Ratio and Quantum Imbalance Vulnerability Score

Abstract

Quantum kernel methods are a candidate approach for machine learning on near-term quantum hardware, but two practical problems limit their deployment: kernel values concentrate exponentially as the qubit count grows, and real-world datasets are often severely class-imbalanced. We present the first systematic empirical study of how these two effects interact. We define two diagnostic metrics, the Discrimination Ratio (DR) and the Quantum Imbalance Vulnerability Score (QIVS), which measure whether quantum kernels retain minority-class separability under concentration. Experiments span ten log-spaced imbalance ratios, five random seeds, five qubit counts (4 to 12), and five real-world datasets, and yield three results. First, DR stays above 1.0 at every qubit count tested (4 to 12), so the discriminative signal survives concentration. Second, at extreme imbalance (IR below 0.003), quantum kernel SVMs retain positive discriminative signal, crossing above DR=1.0 by IR≈0.0028, while the classical oversampling methods SMOTE and ADASYN produce zero minority-class recall throughout the same regime, a practical advantage for quantum kernels at the imbalance extreme. Third, QIVS follows a broadly monotonic decreasing trend, falling from 13.25 to 5.54 as the imbalance ratio increases, with a single minor fluctuation smaller than the cross-seed variability we measure elsewhere in the sweep. This trend makes QIVS a reliable diagnostic for practitioners choosing quantum kernels on imbalanced tasks.