%0 Journal Article
%J Physical Review A
%D 2011
%T Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate
%A Haitan Xu
%A J. M. Taylor
%X Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and sparse representations of quantum information (qubits) and a simple construction of multi-qubit gates, for all anyon models from Chern-Simons-Witten SU(2)$_k$ theory that support universal quantum computation by braiding ($k\geq 3,\ k \neq 4$). In the process, we show how the constructions of topological quantum memory and gates for $k=2,4$ connect naturally to those for $k\geq 3,\ k \neq 4$, unifying these concepts in a simple framework. Furthermore, we illustrate potential extensions of these ideas to other anyon models outside of Chern-Simons-Witten field theory.
%B Physical Review A
%V 84
%8 2011/7/26
%G eng
%U http://arxiv.org/abs/1001.4085v2
%N 1
%! Phys. Rev. A
%R 10.1103/PhysRevA.84.012332