Efficient quantum Gibbs samplers with Kubo--Martin--Schwinger detailed balance condition

TL;DR

This paper develops a family of efficient quantum Gibbs samplers using a finite set of jump operators, building on KMS detailed balance, with simpler implementation and comparable cost to previous methods.

Contribution

It introduces a new class of quantum Gibbs samplers with fewer jump operators, enhancing design flexibility and simplifying implementation compared to prior work.

Findings

Achieves Gibbs sampling with as few as one jump operator.

Maintains quantum simulation cost comparable to existing methods.

Provides a simpler framework with easier error analysis.

Abstract

Lindblad dynamics and other open-system dynamics provide a promising path towards efficient Gibbs sampling on quantum computers. In these proposals, the Lindbladian is obtained via an algorithmic construction akin to designing an artificial thermostat in classical Monte Carlo or molecular dynamics methods, rather than treated as an approximation to weakly coupled system-bath unitary dynamics. Recently, Chen, Kastoryano, and Gily\'en (arXiv:2311.09207) introduced the first efficiently implementable Lindbladian satisfying the Kubo--Martin--Schwinger (KMS) detailed balance condition, which ensures that the Gibbs state is a fixed point of the dynamics and is applicable to non-commuting Hamiltonians. This Gibbs sampler uses a continuously parameterized set of jump operators, and the energy resolution required for implementing each jump operator depends only logarithmically on the precision and the mixing time. In this work, we build upon the structural characterization of KMS detailed balanced Lindbladians by Fagnola and Umanit\`a, and develop a family of efficient quantum Gibbs samplers using a finite set of jump operators (the number can be as few as one), \re{akin to the classical Markov chain-based sampling algorithm. Compared to the existing works, our quantum Gibbs samplers have a comparable quantum simulation cost but with greater design flexibility and a much simpler implementation and error analysis.} Moreover, it encompasses the construction of Chen, Kastoryano, and Gily\'en as a special instance.