← 研踪 PaperTrailarXiv:2609.26788 · v2
Quantum Advantage for Distributed Symmetry Breaking
首次提交 2026-09-23 01:58
版本更新 2026-11-03 22:10
雷达观测 2026-11-04 23:39
摘要
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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v2 · 2026-11-03 22:10 · 最新观测版本
Quantum Advantage for Distributed Symmetry Breaking
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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