Related papers: Compatibility of Braiding and Fusion on Wire Networks

Compatibility of Braiding and Fusion on Wire Networks

URL: http://arxiv.org/abs/2202.08207v1
Date: Wed, 16 Feb 2022 17:28:06 GMT
Title: Compatibility of Braiding and Fusion on Wire Networks
Authors: Aaron Conlon and Joost K Slingerland
Abstract summary: Exchanging particles on graphs, or more concretely on networks of quantum wires, has been proposed as a means to perform fault tolerant quantum computation. We find the usual planar anyons solutions but also more general braid actions. We illustrate this with Abelian, Fibonacci and Ising fusion rules.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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.

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