Deep learning of many-body observables and quantum information scrambling

TL;DR

This paper demonstrates that recurrent neural networks can effectively learn and generalize the dynamics of quantum observables in many-body systems, especially in localized regimes, revealing their potential in quantum information science.

Contribution

It introduces a neural network approach capable of modeling quantum observable dynamics and explores its generalization and extrapolation capabilities across different quantum regimes.

Findings

Recurrent neural networks excel in predicting quantum observable evolution within trained regimes.

The neural network can extrapolate predictions beyond training data in localized regimes.

Classical methods fail in sampling full wave functions where neural networks succeed.

Abstract

Machine learning has shown significant breakthroughs in quantum science, where in particular deep neural networks exhibited remarkable power in modeling quantum many-body systems. Here, we explore how the capacity of data-driven deep neural networks in learning the dynamics of physical observables is correlated with the scrambling of quantum information. We train a neural network to find a mapping from the parameters of a model to the evolution of observables in random quantum circuits for various regimes of quantum scrambling and test its \textit{generalization} and \textit{extrapolation} capabilities in applying it to unseen circuits. Our results show that a particular type of recurrent neural network is extremely powerful in generalizing its predictions within the system size and time window that it has been trained on for both, localized and scrambled regimes. These include regimes where classical learning approaches are known to fail in sampling from a representation of the full wave function. Moreover, the considered neural network succeeds in \textit{extrapolating} its predictions beyond the time window and system size that it has been trained on for models that show localization, but not in scrambled regimes.