Fast Mixing of 1D Quantum Gibbs Samplers at All Temperatures

Recently, quantum computing analogs of classical Gibbs samplers have been introduced—quantum Markov chains that generalize Glauber or Metropolis dynamics, and serve as models of nature’s thermalization process. In this work, we show that every one-dimensional quantum Hamiltonian with short-range interactions admits a quantum Gibbs sampler with a system-size–independent, optimal spectral gap at all finite temperatures. As a consequence, their Gibbs states can be prepared in polylogarithmic depth and exhibit exponential clustering of correlations, extending the classic result of Araki (1969). (Joint work https://arxiv.org/abs/2510.08533 with Thiago Bergamaschi.)