Extracting many-particle entanglement entropy from observables using supervised machine learning

TL;DR

This paper demonstrates that supervised machine learning with convolutional neural networks can accurately infer many-particle entanglement entropy from measurable observables in disordered quantum systems, overcoming measurement challenges.

Contribution

It introduces a neural network approach to estimate entanglement entropy from observables, showing high accuracy and generalization in complex quantum many-particle systems.

Findings

Neural network accurately predicts entanglement entropy in new disorder realizations.

Convolutional neural network outperforms other neural network structures.

Method generalizes well to different parameters within the same phase.

Abstract

Entanglement, which quantifies non-local correlations in quantum mechanics, is the fascinating concept behind much of aspiration towards quantum technologies. Nevertheless, directly measuring the entanglement of a many-particle system is very challenging. Here we show that via supervised machine learning using a convolutional neural network, we can infer the entanglement from a measurable observable for a disordered interacting quantum many-particle system. Several structures of neural networks were tested and a convolutional neural network akin to structures used for image and speech recognition performed the best. After training on a set of 500 realizations of disorder, the network was applied to 200 new realizations and its results for the entanglement entropy were compared to a direct computation of the entanglement entropy. Excellent agreement was found, except for several rare region which in a previous study were identified as belonging to an inclusion of a Griffiths-like quantum phase. Training the network on a test set with different parameters (in the same phase) also works quite well.