The Cross‐Kernel Margin: A Robustness Measure for Quantum Kernel Methods

ABSTRACT Quantum devices in the current noisy intermediate‐scale quantum (NISQ) era are inherently affected by noise, which can degrade the predictive performance of quantum machine learning models. In this work, we introduce a new margin‐based robustness measure for quantum kernel‐assisted support vector machines (QSVMs), termed the cross‐kernel margin . This measure quantifies the stability of a classifier learned under a perturbed kernel relative to the ideal feature space. We derive a posteriori stability bounds for the corresponding inverse squared cross‐kernel margin under kernel perturbations using the Tikhonov‐stabilized SVM dual formulation. The local depolarizing noise model is then applied to this framework to induce perturbations in the kernel. The resulting bounds are numerically checked using simulations across multiple datasets and further tested using kernel matrices obtained from real quantum hardware and a noisy backend simulator. Furthermore, we empirically compare the degradation of test accuracy under local depolarizing noise with the commonly used global depolarizing noise model, providing additional context for the use of the local model in this study. Finally, we present empirical results linking margin‐based quantities with the generalization performance of QSVMs, providing additional motivation for our margin‐based robustness analysis.