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Rapid mixing of quantum spin chains at any finite temperature
Abstract
We prove that a quasi-local quantum Gibbs sampler rapidly mixes to the Gibbs state of any 1D finite-range Hamiltonian at all finite temperatures in 𝒪(log (n/ε)) time. Each update traces out a contiguous block of constant length and reconstructs it using the Petz recovery map, following early proposals for quantum heat-bath Gibbs samplers by Kastoryano and Brandão~\cite{kastoryano2016quantum}. Our proof directly bounds the distance between the updated state and the target Gibbs state using quantum Wasserstein distance of order $1$. We further provide 𝒪(polylog(n/ε)) depth of quantum circuits to prepare these Gibbs states. We hope these techniques will facilitate the analysis and design of other Gibbs samplers.
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BibTeX
@misc{kim2026rapid,
title = {{Rapid mixing of quantum spin chains at any finite temperature}},
author = {Leeseok Kim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01190},
eprint = {2610.01190},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01190},
}
RIS
TY - UNPB
TI - Rapid mixing of quantum spin chains at any finite temperature
AU - Leeseok Kim
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01190
UR - https://arxiv.org/abs/2610.01190
AB - We prove that a quasi-local quantum Gibbs sampler rapidly mixes to the Gibbs state of any 1D finite-range Hamiltonian at all finite temperatures in 𝒪(log (n/ε)) time. Each update traces out a contiguous block of constant length and reconstructs it using the Petz recovery map, following early proposals for quantum heat-bath Gibbs samplers by Kastoryano and Brandão~\cite{kastoryano2016quantum}. Our proof directly bounds the distance between the updated state and the target Gibbs state using quantum Wasserstein distance of order $1$. We further provide 𝒪(polylog(n/ε)) depth of quantum circuits to prepare these Gibbs states. We hope these techniques will facilitate the analysis and design of other Gibbs samplers.
ER -