Quantum Kerr Learning

TL;DR

This paper explores how a single Kerr mode in quantum systems can enhance kernel-based machine learning methods, demonstrating potential improvements in convergence and generalization through theoretical analysis and proposing an experimental protocol.

Contribution

It introduces quantum Kerr learning, a novel approach leveraging Kerr non-linearity for quantum machine learning, supported by theoretical insights and numerical simulations.

Findings

Quantum Kerr modes can improve convergence time.

Quantum Kerr modes can enhance generalization error.

Proposed experimental protocol for implementation.

Abstract

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.