Predicting the von Neumann Entanglement Entropy Using a Graph Neural Network

Abstract

Calculating the von Neumann entanglement entropy from experimental data is challenging due to its dependence on the complete wavefunction, forcing reliance on approximations such as classical mutual information (MI). We propose a machine learning approach using a graph neural network to predict the von Neumann entropy directly from experimentally accessible bitstrings. We test this approach on a Rydberg ladder system and achieve a mean absolute error of $3.6 \times 10^{-3}$ when evaluating within the training range on a dataset with entropy values ranging from 0 to 1.9. The model achieves a mean absolute percentage error of 1.44\% and outperforms MI-based bounds. When tested beyond the training range, the model maintains reasonable accuracy. Furthermore, we demonstrate that fine-tuning the model with small datasets significantly improves performance on data outside the original training range.