Solving Quantum Statistical Mechanics with Variational Autoregressive Networks and Quantum Circuits

TL;DR

This paper introduces a hybrid quantum-classical variational approach combining autoregressive neural networks and quantum circuits to efficiently study quantum statistical mechanics, enabling the calculation of thermal properties and excitation spectra.

Contribution

It presents a novel variational algorithm that jointly optimizes neural networks and quantum circuits for quantum statistical mechanics problems, accessible on near-term quantum devices.

Findings

Successfully computes thermal observables like free energy, entropy, and specific heat.

Provides access to low energy excitation states.

Demonstrates applicability to quantum Ising model with feasible resources.

Abstract

We extend the ability of unitary quantum circuits by interfacing it with classical autoregressive neural networks. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the autoregressive network generates bitstring samples as input states to the quantum circuit. We devise an efficient variational algorithm to jointly optimize the classical neural network and the quantum circuit for quantum statistical mechanics problems. One can obtain thermal observables such as the variational free energy, entropy, and specific heat. As a by product, the algorithm also gives access to low energy excitation states. We demonstrate applications to thermal properties and excitation spectra of the quantum Ising model with resources that are feasible on near-term quantum computers.