Quantum Advantage for Distributed Symmetry Breaking

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.

Quantum Physics (quant-ph); Distributed, Parallel, and Cluster Computing (cs.DC)

arXiv:2609.26788 [quant-ph]

(or arXiv:2609.26788v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.26788 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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