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arXiv · 2307.01171

Quantum Neural Estimation of Entropies

Ziv Goldfeld·Dhrumil Patel·Sreejith Sreekumar·Mark M. Wilde
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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.

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Ziv Goldfeld, Dhrumil Patel, Sreejith Sreekumar, Mark M. Wilde. 2023-07-03. Quantum Neural Estimation of Entropies. https://doi.org/10.1103/physreva.109.032431

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