Variational autoencoder reconstruction of complex many-body physics

TL;DR

This paper demonstrates how variational autoencoders can be used to reconstruct complex many-body quantum states from tomographic data, enabling analysis of quantum phase transitions with deep learning techniques.

Contribution

It introduces a novel application of VAEs for quantum many-body state reconstruction from measurement data, bridging machine learning and quantum physics.

Findings

VAE successfully reconstructs ground-state properties of quantum Ising model.

Method captures quantum phase transition behavior.

Challenges include entropy calculation difficulties.

Abstract

Given the notably increasing complexity of mathematical models to study realistic systems and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models, show limitations in scope or applicability. On the other hand, machine learning, i.e. data-driven, methods prove to be increasingly efficient for the study of complex quantum systems. Deep neural networks in particular have been successfully applied to many-body quantum dynamics simulations and to quantum matter phase characterization. In the present work, we show how to use a variational autoencoder (VAE) -- a state-of-the-art tool in the field of deep learning for the simulation of probability distributions of complex systems. More precisely, we transform a quantum mechanical problem of many-body state reconstruction into a statistical problem, suitable for VAE, by using informationally complete positive operator-valued measure. We show with the paradigmatic quantum Ising model in a transverse magnetic field, that the ground-state physics, such as, e.g., magnetization and other mean values of observables, of a whole class of quantum many-body systems can be reconstructed by using VAE learning of tomographic data, for different parameters of the Hamiltonian, and even if the system undergoes a quantum phase transition. We also discuss challenges related to our approach as entropy calculations pose particular difficulties.