Polynomial-time thermalization and Gibbs sampling from system-bath couplings

TL;DR

This paper proves polynomial-time convergence of certain Lindbladian processes to their steady states, demonstrating efficient quantum thermalization and Gibbs sampling for various complex quantum systems.

Contribution

It introduces a novel method to establish polynomial convergence rates for non-commuting Lindbladians in quantum thermalization and Gibbs sampling.

Findings

Polynomial convergence for high-temperature local lattices.

Efficient Gibbs state preparation via dissipative algorithms.

Lindblad dynamics accurately model thermal relaxation.

Abstract

Many physical phenomena, including thermalization in open quantum systems and quantum Gibbs sampling, are modeled by Lindbladians approximating a system weakly coupled to a bath. Understanding the convergence speed of these Lindbladians to their steady states is crucial for bounding algorithmic runtimes and thermalization timescales. We study two such families of processes: one characterizing a repeated-interaction Gibbs sampling algorithm, and another modeling open many-body quantum thermalization. We prove that both converge in polynomial time for several non-commuting systems, including high-temperature local lattices, weakly interacting fermions, and 1D spin chains. These results demonstrate that simple dissipative quantum algorithms can prepare complex Gibbs states and that Lindblad dynamics accurately capture thermal relaxation. Our proofs rely on a novel technical result that extrapolates spectral gap lower bounds from quasi-local Lindbladians to the non-local generators governing these dynamics.