Quantum Kerr Learning
This work addresses the challenge of leveraging quantum computing for data-driven sciences, though it appears incremental as it builds on existing kernel methods and quantum theories.
The paper tackles the problem of achieving quantum enhancements in kernel-based machine learning methods by demonstrating that a single Kerr mode can improve convergence time and generalization error, supported by theoretical arguments and numerical simulations.
Quantum machine learning is a rapidly evolving field of research that could facilitate important applications for quantum computing and also significantly impact data-driven sciences. In our work, based on various arguments from complexity theory and physics, we demonstrate that a single Kerr mode can provide some "quantum enhancements" when dealing with kernel-based methods. Using kernel properties, neural tangent kernel theory, first-order perturbation theory of the Kerr non-linearity, and non-perturbative numerical simulations, we show that quantum enhancements could happen in terms of convergence time and generalization error. Furthermore, we make explicit indications on how higher-dimensional input data could be considered. Finally, we propose an experimental protocol, that we call \emph{quantum Kerr learning}, based on circuit QED.