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arXiv · 2510.08446

Code Swendsen-Wang Dynamics

Dominik Hangleiter·Nathan Ju·Umesh Vazirani
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Abstract

Recent advances in quantum Gibbs sampling leave open the central question of rapid mixing near and below phase transitions. This challenge is especially relevant for code Hamiltonians whose Gibbs states capture phenomena such as the thermal stability of quantum topological order. In this work, we formulate a new Markov chain, Code Swendsen-Wang dynamics, which uses global updates to prepare the Gibbs states of arbitrary code Hamiltonians. We establish Code Swendsen-Wang dynamics as the right generalization of Swendsen-Wang dynamics for the Ising model to quantum and classical code Hamiltonians: it mixes rapidly for all previously known code Hamiltonians with efficient Gibbs samplers, resolves the central open case of the 4D toric code, and meets fundamental barriers exactly at first-order phase transitions.

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Dominik Hangleiter, Nathan Ju, Umesh Vazirani. 2025-10-09. Code Swendsen-Wang Dynamics. https://arxiv.org/abs/2510.08446

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