Non-Classical Kernels in Continuous Variable Systems

TL;DR

This paper investigates non-classical kernels in continuous-variable quantum systems, demonstrating their potential for quantum advantage in machine learning tasks and clarifying the role of phase space correlations.

Contribution

It introduces a kernel nonclassicality witness based on phase space methods and explores its implications for quantum advantage in parameter estimation.

Findings

Non-classical kernels can outperform classical kernels in quantum machine learning.

Imperfect state preparation affects the kernel's nonclassicality and performance.

Non-classical kernels enable quantum advantage in parameter estimation tasks.

Abstract

Kernel methods are ubiquitous in classical machine learning, and recently their formal similarity with quantum mechanics has been established. To grasp the potential advantage of quantum machine learning, it is necessary to understand the distinction between non-classical kernel functions and classical kernels. This paper builds on a recently proposed phase space nonclassicality witness [Bohmann, Agudelo, Phys. Rev. Lett. 124, 133601 (2020)] to derive a witness for the kernel's quantumness in continuous-variable systems. We discuss the role of kernel's nonclassicality in data distribution in the feature space and the effect of imperfect state preparation. Furthermore, we show that the non-classical kernels lead to the quantum advantage in parameter estimation. Our work highlights the role of the phase space correlation functions in understanding the distinction between classical machine learning from quantum machine learning.