Quantum Neural Estimation of Entropies

TL;DR

This paper introduces a variational quantum algorithm that combines quantum circuits and neural networks to estimate various quantum entropy measures, demonstrating promising accuracy in simulations.

Contribution

It presents a novel hybrid quantum-classical variational approach for estimating multiple quantum entropy measures, including von Neumann and Rènyi entropies.

Findings

Accurate entropy estimates in noiseless simulations

Versatile approach applicable to different entropy measures

Potential for use in quantum information processing tasks

Abstract

Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy measures. Here we propose a variational quantum algorithm for estimating the von Neumann and R\'enyi entropies, as well as the measured relative entropy and measured R\'enyi relative entropy. Our approach first parameterizes a variational formula for the measure of interest by a quantum circuit and a classical neural network, and then optimizes the resulting objective over parameter space. Numerical simulations of our quantum algorithm are provided, using a noiseless quantum simulator. The algorithm provides accurate estimates of the various entropy measures for the examples tested, which renders it as a promising approach for usage in downstream tasks.