线网络上编织与融合的相容性
Compatibility of Braiding and Fusion on Wire Networks
AI总结：
本文研究量子线网络上粒子交换的图辫群结构，通过要求编织与拓扑荷融合相容导出广义六边形方程，发现除平面任意子解外还存在更一般的编织作用，并用阿贝尔、斐波那契和伊辛融合规则加以说明。
摘要：
在图上交换粒子，或更具体地说在量子线网络上交换粒子，已被提出作为实现容错量子计算的一种手段。这一想法受到平面系统中任意子编织的启发。然而，图上的交换并不由通常的辫群支配，而是由图辫群支配。通过要求图编织与拓扑荷融合相容，我们得到了广义六边形方程。我们发现通常的平面任意子解仍然存在，但也出现了更一般的编织作用。我们用阿贝尔、斐波那契和伊辛融合规则对此进行了说明。
英文摘要：
Exchanging particles on graphs, or more concretely on networks of quantum wires, has been proposed as a means to perform fault tolerant quantum computation. This was inspired by braiding of anyons in planar systems. However, exchanges on a graph are not governed by the usual braid group but instead by a graph braid group. By imposing compatibility of graph braiding with fusion of topological charges, we obtain generalized hexagon equations. We find the usual planar anyons solutions but also more general braid actions. We illustrate this with Abelian, Fibonacci and Ising fusion rules.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
