5 papers · 1 filter
Fusion rules for permutation extensions of modular tensor categories
Colleen Delaney
We give a construction and algorithmic description of the fusion ring of permutation extensions of an arbitrary modular tensor category using a combinatorial approach inspired by t…
Symmetry defects and their application to topological quantum computing
Colleen Delaney, Zhenghan Wang
We describe the mathematical theory of topological quantum computing with symmetry defects in the language of fusion categories and unitary representations. Symmetry defects togeth…
On invariants of Modular categories beyond modular data
Parsa Bonderson, Colleen Delaney, César Galindo +3
We study novel invariants of modular categories that are beyond the modular data, with an eye towards a simple set of complete invariants for modular categories. Our focus is on th…
A systematic search of knot and link invariants beyond modular data
Colleen Delaney, Alan Tran
The smallest known example of a family of modular categories that is not determined by its modular data are the rank 49 categories for $G=\mathbb{Z}_{…
Local unitary representations of the braid group and their applications to quantum computing
Colleen Delaney, Eric C. Rowell, Zhenghan Wang
We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander…