01255nas a2200133 4500008004100000245010500041210006900146260001400215490000700229520081400236100001501050700001901065856003701084 2011 eng d00aUnified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate0 aUnified approach to topological quantum computation with anyons c2011/7/260 v843 aTopological 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.
1 aXu, Haitan1 aTaylor, J., M. uhttp://arxiv.org/abs/1001.4085v2