In topological quantum computing, information is encoded in “knotted” quantum states of
topological phases of matter, thus being locked into topology to prevent decay. Topological …

We describe several methods of constructing R-matrices that are dependent upon many
parameters, for example unitary R-matrices and R-matrices whose entries are functions. As …

A bstract In order to examine the simulation of integrable quantum systems using quantum
computers, it is crucial to first classify Yang-Baxter operators. Hietarinta was among the first …

We introduce and study a class of anyon models that are a natural generalization of Ising
anyons and Majorana fermion zero modes. These models combine an Ising anyon sector …

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 the …

We provide a mathematical definition of a low energy scaling limit of a sequence of general
non-relativistic quantum theories in any dimension, and apply our formalism to anyonic …

We develop a theory of localization for braid group representations associated with objects
in braided fusion categories and, more generally, to Yang–Baxter (YB) operators in …

We study representations of the loop braid group LBn from the perspective of extending
representations of the braid group n. We also pursue a generalization of the braid/Hecke …

For non-abelian simple objects in a unitary modular category, the density of their braid group
representations, the# P-hard evaluation of their associated link invariants, and the BQP …

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 …