Quantum Advantage for Distributed Symmetry Breaking

2026-09-22

AI Summary

本文提出了一种分布式量子算法，能在常数轮内解决3-着色环问题及其它局部可检查的标记问题，展示了量子算法在分布式计算中的优势。

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.

Problem

• Distributed Quantum Algorithm
• Locally Checkable Labeling Problems (LCLs)
• Quantum Advantage
• LOCAL Model
• Graph Problems

Innovation

• distributed quantum algorithm
• 3-coloring cycles
• LOCAL model
• quantum-LOCAL model
• asymptotic distributed quantum advantage