Machine Learning Universally Maps Nonlocal Quantum Entropy Via Second-order Local Correlations In Nonequilibrium States

Understanding the nonlocal properties of quantum states presents a significant hurdle in advancing large-scale quantum computation and simulation, and Hao Liao, Xuanqin Huang, and Ping Wang from Shenzhen University and Beijing Normal University have now made a crucial step towards overcoming it. The team demonstrates a powerful new method for determining quantum mutual information, a key measure of entanglement, even in complex, nonequilibrium quantum systems. Their approach utilises a multilayer perceptron to establish a direct link between quantum mutual information and readily measurable local correlations, offering a practical pathway for experimental determination of entanglement in platforms currently under development. This achievement not only simplifies the characterisation of complex quantum states, but also establishes a general framework for reconstructing other important nonlocal observables, paving the way for deeper insights into phenomena such as many-body localisation and thermalisation.

Quantum mutual information (QMI), a fundamental measure of quantum correlations, indicates this nonlocality, but calculating it directly presents challenges for complex quantum systems. The research team developed a method to accurately estimate QMI using only local correlations observable in the quantum state, avoiding computationally expensive global measurements. This approach reconstructs the full quantum state from its reduced density matrices, effectively capturing nonlocal entropy through locally accessible information.

The team demonstrates that this method accurately estimates QMI for various quantum states, including those with strong entanglement and complex correlations. Furthermore, the research establishes a direct relationship between local correlations and nonlocal entropy, providing a new way to characterize and understand the fundamental properties of quantum systems. This advancement enables efficient analysis of quantum states in complex scenarios, paving the way for improved quantum algorithms and simulations.

Machine Learning Reveals MBL Entanglement Structure

This research addresses a central challenge in understanding many-body localization (MBL), a phenomenon where disorder prevents thermalization in quantum systems. Characterizing the complex entanglement structure that emerges in MBL systems is difficult using traditional methods. The authors explore machine learning, specifically neural networks, to predict quantum properties like entanglement entropy from local measurements, offering a significant shift from directly calculating complex quantities. The authors propose a machine learning framework that learns the relationship between local correlations and non-local entanglement entropy, demonstrating its universal applicability.

They utilize neural networks to map local observables to entanglement entropy, generating training data from numerical simulations of disordered quantum systems. The performance of their model is rigorously evaluated, comparing its predictions to direct calculations of entanglement entropy. The model demonstrates generalization to different system sizes and disorder strengths, indicating it has learned a fundamental relationship rather than simply memorizing data.

Machine Learning Predicts Quantum Mutual Information Accurately

This research presents a new machine learning framework, based on multilayer perceptrons, for efficiently predicting quantum mutual information (QMI) in complex quantum systems. Scientists successfully demonstrated the ability to accurately determine QMI, a key measure of entanglement, by analyzing only readily accessible second-order correlations, thus avoiding the need for complete quantum state tomography. This method proved effective in capturing the dynamic behaviour of QMI across both many-body localized and thermalizing regimes, significantly outperforming conventional computational techniques. Notably, the trained machine learning model exhibits universality, accurately predicting QMI dynamics across a wide range of disorder strengths and time scales, even beyond those used during its initial training.

This suggests an underlying universal relationship between low-order correlations and non-local quantum properties. The approach also demonstrates robustness against realistic measurement noise, indicating its practical feasibility in experimental platforms. Researchers anticipate extending this framework to higher dimensions, long-range interaction models, and open quantum systems.