Thermalization in Nature and on a Quantum Computer

TL;DR

This paper explores how thermal states naturally emerge in quantum systems and introduces a quantum algorithm for efficiently preparing Gibbs states with guaranteed runtime and error bounds.

Contribution

It presents a new perturbation theorem applicable in the thermodynamic limit and a general quantum algorithm for Gibbs state preparation with certified performance.

Findings

Thermalization occurs under specific conditions in quantum many-body systems.

A novel perturbation theorem for weak system-bath couplings is introduced.

A quantum algorithm for Gibbs state preparation with proven runtime and error bounds is developed.

Abstract

In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound. This complements quantum Metropolis algorithms, which are expected to be efficient but have no known runtime estimates and only work for local Hamiltonians.