A Variational Quantum Algorithm for Preparing Quantum Gibbs States

TL;DR

This paper introduces a practical variational quantum algorithm for preparing Gibbs states by approximating the logarithm with Fourier series, enabling efficient thermal state preparation on near-term quantum computers.

Contribution

It proposes a novel variational method based on free energy minimization using Fourier series, suitable for high-temperature Gibbs states on near-term quantum devices.

Findings

Efficient for high-temperature Gibbs states with close initial parameters

Uses Fourier series to estimate entropy component via simple measurements

Numerical validation on five-qubit Hamiltonians shows viability

Abstract

Preparation of Gibbs distributions is an important task for quantum computation. It is a necessary first step in some types of quantum simulations and further is essential for quantum algorithms such as quantum Boltzmann training. Despite this, most methods for preparing thermal states are impractical to implement on near-term quantum computers because of the memory overheads required. Here we present a variational approach to preparing Gibbs states that is based on minimizing the free energy of a quantum system. The key insight that makes this practical is the use of Fourier series approximations to the logarithm that allows the entropy component of the free-energy to be estimated through a sequence of simpler measurements that can be combined together using classical post processing. We further show that this approach is efficient for generating high-temperature Gibbs states, within constant error, if the initial guess for the variational parameters for the programmable quantum circuit are sufficiently close to a global optima. Finally, we examine the procedure numerically and show the viability of our approach for five-qubit Hamiltonians using Trotterized adiabatic state preparation as an ansatz.