Sampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computer

TL;DR

This paper introduces a quantum algorithm for preparing thermal Gibbs states and evaluating partition functions, with bounds on thermalization time related to system properties, advancing quantum simulation capabilities.

Contribution

It presents a universal bound on thermalization time and an efficient algorithm for partition function evaluation on quantum computers, linking physical properties to computational complexity.

Findings

Thermalization time bounded by D^alpha, with alpha < 1/2.

Partition function evaluation time proportional to thermalization time.

Algorithm efficiency depends on system's free energy density.

Abstract

We present a quantum algorithm to prepare the thermal Gibbs state of interacting quantum systems. This algorithm sets a universal upper bound D^alpha on the thermalization time of a quantum system, where D is the system's Hilbert space dimension and alpha < 1/2 is proportional to the Helmholtz free energy density of the system. We also derive an algorithm to evaluate the partition function of a quantum system in a time proportional to the system's thermalization time and inversely proportional to the targeted accuracy squared.