Local unitary representations of the braid group and their applications   to quantum computing
  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 polynomial. Then we discuss the Jones representation and Jones polynomial and their application to anyonic quantum computation. Finally we outline the approximation of the Jones polynomial and explicit localizations of braid group representations. 
Colleen Delaney, Eric C. Rowell and Zhenghan Wang
math.QA