Quantum Kernel Methods for High-Dimensional Generalization: Separating Quantum Advantage from Classical Simulability
Senegal Senegal Senegal 
Abstract
Quantum kernel methods have emerged as a promising approach for exploiting quantum feature representations to improve learning performance in high-dimensional classification tasks. Increasing advances in quantum computing have stimulated expectations of quantum advantage; however, distinguishing genuine quantum computational benefits from efficient classical simulability remains a fundamental challenge. This study aimed to evaluate the effectiveness of quantum kernel methods for high-dimensional generalization while identifying computational conditions under which quantum learning exceeds the capability of advanced classical approximation techniques. A mixed-methods sequential explanatory design was employed using 18,000 large-scale computational experiments complemented by benchmark datasets, quantum algorithm implementation records, computational complexity analyses, and expert evaluations. Quantitative data were analyzed through generalized linear mixed-effects modeling, Monte Carlo uncertainty estimation, multivariate regression, sensitivity analysis, and cross-validation, whereas qualitative evidence was interpreted using thematic analysis of technical documentation and expert perspectives. Findings demonstrated that quantum kernel methods achieved superior generalization when highly expressive quantum feature maps generated representations resistant to efficient classical simulation while maintaining robust statistical learning performance. Classical approximation algorithms successfully reproduced several shallow quantum kernels, indicating that predictive accuracy alone does not establish authentic quantum advantage. Results suggest that meaningful quantum superiority arises from the integrated interaction among feature-map expressivity, computational complexity, statistical generalization, and limited classical simulability. The proposed framework provides a rigorous foundation for evaluating scalable quantum machine learning systems and guiding the development of future fault-tolerant quantum artificial intelligence.
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Copyright (c) 2026 Amadou Ba, Ndeye Ndour, Oumar Gueye
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