Quantum Neural Estimation of Entropies

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 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.

14 pages, 2 figures; see also independent works of Shin, Lee, and Jeong at arXiv:2306.14566v1 and Lee, Kwon, and Lee at arXiv:2307.13511v2

References in corpus (10)

• Exploiting symmetry in variational quantum machine learning
• Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines
• Mitigating Barren Plateaus with Transfer-learning-inspired Parameter Initializations
• Quantum algorithms for estimating quantum entropies
• Multivariate trace estimation in constant quantum depth
• Quantum Mixed State Compiling
• Quantum Phase Processing and its Applications in Estimating Phase and Entropies
• Phase transition in Stabilizer Entropy and efficient purity estimation
• An Improved Sample Complexity Lower Bound for (Fidelity) Quantum State Tomography
• Estimating Quantum Mutual Information Through a Quantum Neural Network

Cited by in corpus (5)

• New Quantum Algorithms for Computing Quantum Entropies and Distances
• QSlack: A slack-variable approach for variational quantum semi-definite programming
• Mutual information maximizing quantum generative adversarial networks
• Disentangling quantum neural networks for unified estimation of quantum entropies and distance measures
• Performance Guarantees for Quantum Neural Estimation of Entropies