Rapid mixing of quantum spin chains at any finite temperature

Leeseok Kim

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arXiv · 2610.01190

Rapid mixing of quantum spin chains at any finite temperature

Leeseok Kim

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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 $\mathcal{O}\left(\log (n/\varepsilon)\right)$ 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 $\mathcal{O}(\text{polylog}(n/\varepsilon))$ 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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Leeseok Kim. 2026-10-01. Rapid mixing of quantum spin chains at any finite temperature. https://arxiv.org/abs/2610.01190

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