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arXiv · 2609.26788

Quantum Advantage for Distributed Symmetry Breaking

Maxime Flin·Longcheng Li·Jukka Suomela
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Abstract

We present a distributed quantum algorithm that $3$-colors cycles in $O(1)$ rounds, with high probability. It follows that all locally checkable labeling problems (LCLs) that have round complexity $O(\log^* n)$ in the classical LOCAL model can be solved in $O(1)$ rounds in the quantum-LOCAL model, with high probability; this includes problems such as maximal independent set and maximal matching in bounded-degree graphs. This presents the first natural examples of graph problems with an asymptotic distributed quantum advantage for the LOCAL model; all prior examples that separate LOCAL and quantum-LOCAL are artificial problems constructed merely for the sake of demonstrating quantum advantage.

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Maxime Flin, Longcheng Li, Jukka Suomela. 2026-09-22. Quantum Advantage for Distributed Symmetry Breaking. https://arxiv.org/abs/2609.26788

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