Quantum Neural Estimation of Entropies
This work addresses the challenge of entropy estimation in quantum systems, which is crucial for quantum information processing, but it appears incremental as it builds on existing variational methods.
The authors tackled the problem of estimating entropy measures for unknown quantum states using only available copies, by proposing a variational quantum algorithm that combines quantum circuits and classical neural networks to estimate von Neumann, Rényi, and measured relative entropies. Numerical simulations on a noiseless quantum simulator showed accurate estimates for tested examples, making it promising for downstream tasks.
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 Rényi entropies, as well as the measured relative entropy and measured Rényi 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.