Revealing quantum chaos with machine learning

Journal article (2020)

Authors

Y. A. Kharkov Russian Quantum Center, Moscow, University of New South Wales, University of Maryland
V. E. Sotskov Russian Quantum Center, Moscow
A. Karazeev QID/Wehner Group - QuTech Advanced Research Centre , QuTech Advanced Research Centre, Moscow Institute of Physics and Technology
E. O. Kiktenko Russian Quantum Center, Moscow, Russian Academy of Sciences, National University of Science and Technology MISiS
A Fedorov QN/Quantum Transport , Moscow Institute of Physics and Technology
Research Group
QID/Wehner Group (QuTech Advanced Research Centre) (TU Delft)
Copyright: © 2020 Y. A. Kharkov, V. E. Sotskov, A. Karazeev, E. O. Kiktenko, A Fedorov
DOI: https://doi.org/10.1103/PhysRevB.101.064406
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Published Date

2020

Language

English

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Faculty

QuTech Advanced Research Centre

Department

Quantum Internet Division

Research Group

QID/Wehner Group

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 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.