Accelerating quantum Gibbs sampling without quantum walks

TL;DR

This paper introduces a walk-free quantum algorithm for preparing Gibbs states with quadratic spectral-gap dependence improvement, applicable to a broad class of quantum Gibbs samplers satisfying detailed balance.

Contribution

It provides a novel factorization of the parent Hamiltonian enabling singular-value filtering, avoiding quantum walks for Gibbs state preparation.

Findings

Quadratic improvement in spectral-gap dependence for Gibbs sampling.

Applicable to multiple efficient Gibbs samplers beyond Davies.

Introduces auxiliary dissipative dynamics for warm starts.

Abstract

Szegedy's quantum walk gives a generic quadratic speedup for reversible classical Markov chains, but extending this mechanism to quantum Gibbs sampling has remained challenging beyond special cases. We present a walk-free quantum algorithm for preparing purified Gibbs states with a quadratic improvement in spectral-gap dependence for a broad class of quantum Gibbs samplers that satisfy exact Kubo-Martin-Schwinger detailed balance. Our main structural result is an explicit factorization of the corresponding parent Hamiltonian into noncommutative first-order operators. This turns purified Gibbs-state preparation into a singular-value filtering problem and enables a quantum singular value transformation algorithm with quadratically improved gap dependence under standard coherent-access assumptions. The framework applies to several efficiently implementable Gibbs samplers beyond the Davies setting. We also introduce an auxiliary dissipative dynamics based on the same factorization, which can be used to generate warm starts in the doubled Hilbert space in metastable regimes.