Quantum Kernel Methods: Convergence Theory, Separation Bounds and Applications to Marketing Analytics

Abstract This work studies the feasibility of applying quantum kernel methods to a real con- sumer classification task in the NISQ regime. We present a hybrid pipeline that combines a quantum-kernel Support Vector Machine (Q-SVM) with a quantum feature extraction mod- ule (QFE), and benchmark it against classical and quantum baselines in simulation and with limited shallow-depth hardware runs. With fixed hyperparameters, the proposed Q-SVM attains 0.7790 accuracy, 0.7647 precision, 0.8609 recall, 0.8100 F1, and 0.83 ROC AUC, ex- hibiting higher sensitivity while maintaining competitive precision relative to classical SVM. We interpret these results as an initial indicator and a concrete starting point for NISQ-era workflows and hardware integration, rather than a definitive benchmark. Methodologically, our design aligns with recent work that formalizes quantum–classical separations and verifies resources via XEB-style approaches, motivating shallow yet expressive quantum embeddings to achieve robust separability despite hardware noise constraints.