分布式对称破缺的量子优势

中文摘要 AI 辅助

我们提出了一种分布式量子算法，能够以高概率在 $O(1)$ 轮内对环进行 $3$-着色。由此可知，所有在经典 LOCAL 模型中具有 $O(\log^* n)$ 轮复杂度的局部可检查标记问题（LCLs）都可以在量子-LOCAL 模型中以高概率在 $O(1)$ 轮内解决；这包括有界度图中的最大独立集和最大匹配等问题。这首次为 LOCAL 模型提供了具有渐近分布式量子优势的自然图问题实例；此前所有区分 LOCAL 与量子-LOCAL 的示例均为仅为展示量子优势而构造的人为问题。

英文摘要

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.

发表机构

• Aalto University（阿尔托大学）
• University of Cambridge（剑桥大学）

机构由 AI 辅助整理，请以论文原文为准。