Quantum kernel methods for marketing analytics with convergence theory and separation bounds

This work studies the feasibility of applying quantum kernel methods to a real consumer 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 module (QFE), and benchmark it against classical and quantum baselines in simulation (hardware validation remains future work). Hyperparameters were selected via nested cross-validation on the training partition and then fixed for test evaluation; under these settings, the proposed Q-SVM attains 0.7790 accuracy, 0.7647 precision, 0.8609 recall, 0.8100 F1, and 0.83 ROC AUC, exhibiting higher sensitivity while maintaining competitive precision relative to classical SVM. All headline metrics are obtained via high-fidelity simulation. 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 (Cross-Entropy Benchmarking) approaches, motivating shallow yet expressive quantum embeddings to achieve robust separability despite hardware noise constraints.