Topological Quantum Compiling
01 January 2007
A method for compiling quantum algorithms into specific braiding patterns for Fibonacci anyons is developed. Qubits are encoded into triplets of quasiparticles and single qubit gates are carried out by braiding quasiparticles within qubits. Two qubit gates are carried out by "weaving" either a pair of particles or a single particle from one qubit through the quasiparticles forming the second qubit which remain stationary. All gate constructions are built out of three-braids which can be efficiently compiled and improved to any required accuracy using the Solovay-Kitaev algorithm.