Estimating Quantum Mutual Information Through a Quantum Neural Network

TL;DR

This paper introduces QMINE, a quantum neural network-based method for estimating von Neumann entropy and quantum mutual information, leveraging quantum Donsker-Varadhan representation and parameter shift rules for efficient quantum data processing.

Contribution

The paper presents a novel quantum neural network approach, QMINE, with a new quantum Donsker-Varadhan representation for accurate quantum entropy estimation.

Findings

Numerical results support the effectiveness of QMINE.

QMINE outperforms classical methods in processing quantum datasets.

Quantum Donsker-Varadhan representation improves entropy estimation accuracy.

Abstract

We propose a method of quantum machine learning called quantum mutual information neural estimation (QMINE) for estimating von Neumann entropy and quantum mutual information, which are fundamental properties in quantum information theory. The QMINE proposed here basically utilizes a technique of quantum neural networks (QNNs), to minimize a loss function that determines the von Neumann entropy, and thus quantum mutual information, which is believed more powerful to process quantum datasets than conventional neural networks due to quantum superposition and entanglement. To create a precise loss function, we propose a quantum Donsker-Varadhan representation (QDVR), which is a quantum analog of the classical Donsker-Varadhan representation. By exploiting a parameter shift rule on parameterized quantum circuits, we can efficiently implement and optimize the QNN and estimate the quantum entropies using the QMINE technique. Furthermore, numerical observations support our predictions of QDVR and demonstrate the good performance of QMINE.