Variational Quantum Algorithms for Gibbs State Preparation

TL;DR

This paper reviews variational quantum algorithms for preparing Gibbs states on NISQ devices, compares different methods, and benchmarks a recent algorithm on a quantum spin model to evaluate its performance.

Contribution

It provides a concise overview of Gibbs state preparation algorithms and benchmarks a recent variational approach on a specific quantum model.

Findings

The benchmark demonstrates the effectiveness of the variational algorithm on the XY model.

Different algorithms vary in efficiency and accuracy for Gibbs state preparation.

The study highlights the potential of VQAs for thermodynamic simulations on NISQ devices.

Abstract

Preparing the Gibbs state of an interacting quantum many-body system on noisy intermediate-scale quantum (NISQ) devices is a crucial task for exploring the thermodynamic properties in the quantum regime. It encompasses understanding protocols such as thermalization and out-of-equilibrium thermodynamics, as well as sampling from faithfully prepared Gibbs states could pave the way to providing useful resources for quantum algorithms. Variational quantum algorithms (VQAs) show the most promise in effciently preparing Gibbs states, however, there are many different approaches that could be applied to effectively determine and prepare Gibbs states on a NISQ computer. In this paper, we provide a concise overview of the algorithms capable of preparing Gibbs states, including joint Hamiltonian evolution of a system-environment coupling, quantum imaginary time evolution, and modern VQAs utilizing the Helmholtz free energy as a cost function, among others. Furthermore, we perform a benchmark of one of the latest variational Gibbs state preparation algorithms, developed by Consiglio et al. (arXiv:2303.11276), by applying it to the spin 1/2 one-dimensional $XY$ model.