Layerwise Quantum Convolutional Neural Networks Provide a Unified Way for Estimating Fundamental Properties of Quantum Information Theory

• DOI: 10.48550/arxiv.2401.07716
• Publication Date: 2024-01-01
• Authors: Myeongjin Shin; Seung-Woo Lee; Mingyu Lee; Donghwa Ji; Hyeonjun Yeo; Harrison J. Lee; Kabgyun Jeong
• Keywords: Kullback–Leibler divergence; Entropy estimation; Information Theory

The estimation of fundamental properties in quantum information theory, including von Neumann entropy, R\'enyi Tsallis relative trace distance, and fidelity, has received significant attention. While various algorithms exist for individual property estimation, a unified approach is lacking. This paper proposes methodology using Layerwise Quantum Convolutional Neural Networks (LQCNN). Recent studies exploring parameterized circuits face challenges such as barren plateaus complexity issues large qubit states. In contrast, our work overcomes these challenges, avoiding providing practical solution Our first contribution offers mathematical proof that the LQCNN structure preserves properties. Furthermore, second analyzes algorithm's complexity, demonstrating its avoidance through structured local cost function.