Artificial Neural Network Based Computation for Out-of-Time-Ordered Correlators

TL;DR

This paper introduces a machine learning approach using restricted-Boltzmann-machines to efficiently compute out-of-time-ordered correlators in complex quantum many-body systems, demonstrating promising results in a 2D Ising model.

Contribution

The paper presents a novel machine learning method for calculating OTOCs applicable to high-dimensional, highly entangled quantum systems, overcoming traditional computational challenges.

Findings

Successfully computed early-time OTOCs in a 2D Ising model

Demonstrated applicability to arbitrary-dimensional systems

Showed potential for future quantum physics studies

Abstract

Out-of-time-ordered correlators (OTOCs) are of crucial importance for studying a wide variety of fundamental phenomena in quantum physics, ranging from information scrambling to quantum chaos and many-body localization. However, apart from a few special cases, they are notoriously difficult to compute even numerically due to the exponential complexity of generic quantum many-body systems. In this paper, we introduce a machine learning approach to OTOCs based on the restricted-Boltzmann-machine architecture, which features wide applicability and could work for arbitrary-dimensional systems with massive entanglement. We show, through a concrete example involving a two-dimensional transverse field Ising model, that our method is capable of computing early-time OTOCs with respect to random pure quantum states or infinite-temperature thermal ensembles. Our results showcase the great potential for machine learning techniques in computing OTOCs, which open up numerous directions for future studies related to similar physical quantities.