Enhancing Quantum Machine Learning: The Power of Non-Linear Optical Reproducing Kernels

Abstract: Amidst the array of quantum machine learning algorithms, the quantum kernel method has emerged as a focal point, primarily owing to its compatibility with noisy intermediate-scale quantum devices and its promise to achieve quantum advantage. This method operates by nonlinearly transforming data into feature space constructed with quantum states, enabling classification and regression tasks. In this study, we present a novel feature space constructed using Kerr coherent states, which generalize su(2), su(1, 1) coherent states, and squeezed states. Notably, the feature space exhibits constant curvature, comprising both spherical and hyperbolic geometries, depending on the sign of the Kerr parameter. Remarkably, the physical parameters associated with the coherent states, enable control over the curvature of the feature space. Our study employs Kerr kernels derived from encoding data into the phase and amplitude of Kerr coherent states. We analyze various datasets ranging from Moon to breast cancer diagnostics. Our findings demonstrate the robustness of Kerr coherent states, attributed to their flexibility in accommodating different hyperparameters, thereby offering superior performance across noisy datasets and hardware setups.