Distributed Quantum Advantage in Locally Checkable Labeling Problems

Abstract:In this paper, we present the first known example of a locally checkable labeling problem (LCL) that admits asymptotic distributed quantum advantage in the LOCAL model of distributed computing: our problem can be solved in $O(\log n)$ communication rounds in the quantum-LOCAL model, but it requires $\Omega(\log n \cdot \log^{0.99} \log n)$ communication rounds in the classical randomized-LOCAL model. We also show that distributed quantum advantage cannot be arbitrarily large: if an LCL problem can be solved in $T(n)$ rounds in the quantum-LOCAL model, it can also be solved in $\tilde O(\sqrt{n T(n)})$ rounds in the classical randomized-LOCAL model. In particular, a problem that is strictly global classically is also almost-global in quantum-LOCAL. Our second result also holds for $T(n)$-dependent probability distributions. As a corollary, if there exists a finitely dependent distribution over valid labelings of some LCL problem $\Pi$, then the same problem $\Pi$ can also be solved in $\tilde O(\sqrt{n})$ rounds in the classical randomized-LOCAL and deterministic-LOCAL models. That is, finitely dependent distributions cannot exist for global LCL problems.

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

arXiv:2504.05191 [cs.DC]

(or arXiv:2504.05191v2 [cs.DC] for this version)

https://doi.org/10.48550/arXiv.2504.05191 Focus to learn more arXiv-issued DOI via DataCite

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