Statistical Mechanics Calculations Using Variational Autoregressive Networks and Quantum Annealing

TL;DR

This paper introduces a new approximation method combining quantum annealing samples with variational autoregressive networks to improve the accuracy of partition function calculations in statistical mechanics.

Contribution

It presents a novel approach that integrates quantum annealing data with VAN, enhancing approximation accuracy over existing methods.

Findings

Improved accuracy in partition function estimation for the Sherrington-Kirkpatrick model.

Demonstrated advantages over traditional VAN and naive mean field methods.

Empirical validation using quantum annealing samples.

Abstract

In statistical mechanics, computing the partition function is generally difficult. An approximation method using a variational autoregressive network (VAN) has been proposed recently. This approach offers the advantage of directly calculating the generation probabilities while obtaining a significantly large number of samples. The present study introduces a novel approximation method that employs samples derived from quantum annealing machines in conjunction with VAN, which are empirically assumed to adhere to the Gibbs-Boltzmann distribution. When applied to the finite-size Sherrington-Kirkpatrick model, the proposed method demonstrates enhanced accuracy compared to the traditional VAN approach and other approximate methods, such as the widely utilized naive mean field.