Conlon, Aaron and Slingerland, J. K. (2023) Compatibility of braiding and fusion on wire networks. Physical Review B, 108 (3). ISSN 1098-0121

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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.

Item Type:	Article
Keywords:	graph braid group; anyons; topological quantum computation; braid group;
Academic Unit:	Faculty of Science and Engineering > Theoretical Physics
Item ID:	17814
Identification Number:	https://doi.org/10.1103/PhysRevB.108.035150
Depositing User:	IR Editor
Date Deposited:	10 Nov 2023 11:51
Journal or Publication Title:	Physical Review B
Publisher:	American Physical Society
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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