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The estimation of fundamental properties in quantum information theory,including von Neumann entropy, R\'enyi entropy, Tsallis entropy, quantumrelative entropy, trace distance, and fidelity, has received significantattention. While various algorithms exist for individual property estimation, aunified approach is lacking. This paper proposes a unified methodology usingLayerwise Quantum Convolutional Neural Networks (LQCNN). Recent studiesexploring parameterized quantum circuits for property estimation facechallenges such as barren plateaus and complexity issues in large qubit states.In contrast, our work overcomes these challenges, avoiding barren plateaus andproviding a practical solution for large qubit states. Our first contributionoffers a mathematical proof that the LQCNN structure preserves fundamentalproperties. Furthermore, our second contribution analyzes the algorithm'scomplexity, demonstrating its avoidance of barren plateaus through a structuredlocal cost function.

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