Quantum Kerr Learning

Quantum machine learning is a rapidly evolving area that could facilitate important applications for quantum computing and significantly impact data science. In our work, we argue that a single Kerr mode might provide some extra quantum enhancements when using quantum kernel methods based on various reasons from complexity theory and physics. Furthermore, we establish an experimental protocol, which we call \emph{quantum Kerr learning} based on circuit QED. A detailed study using the kernel method, neural tangent kernel theory, first-order perturbation theory of the Kerr non-linearity, and non-perturbative numerical simulations, shows quantum enhancements could happen in terms of the convergence time and the generalization error, while explicit protocols are also constructed for higher-dimensional input data.