# Revealing quantum chaos with machine learning

## TL;DR

This paper demonstrates how machine learning techniques, including neural networks and autoencoders, can classify quantum regimes, detect anomalies, and identify phase transitions in quantum many-body systems with high accuracy.

## Contribution

It introduces novel machine learning applications for classifying quantum chaos, detecting quantum scars, and pinpointing phase transitions in complex quantum systems.

## Key findings

- Neural networks accurately classify regular and chaotic quantum billiards.
- Variational autoencoders detect anomalous quantum states like scars.
- Machine learning reveals the transition from integrability to chaos in spin chains.

## Abstract

Understanding properties of quantum matter is an outstanding challenge in science. In this paper, we demonstrate how machine-learning methods can be successfully applied for the classification of various regimes in single-particle and many-body systems. We realize neural network algorithms that perform a classification between regular and chaotic behavior in quantum billiard models with remarkably high accuracy. We use the variational autoencoder for autosupervised classification of regular/chaotic wave functions, as well as demonstrating that variational autoencoders could be used as a tool for detection of anomalous quantum states, such as quantum scars. By taking this method further, we show that machine learning techniques allow us to pin down the transition from integrability to many-body quantum chaos in Heisenberg XXZ spin chains. For both cases, we confirm the existence of universal W shapes that characterize the transition. Our results pave the way for exploring the power of machine learning tools for revealing exotic phenomena in quantum many-body systems.