Fault-tolerance for a universal non-Abelian topological quantum computer at finite temperature*

We study a quantum memory constructed as a two-dimensional phenomenological model of Fibonacci anyons on a torus, in the presence of thermal noise represented by pair-creation processes and measurement errors. The correction procedure is based on the cellular automaton decoders originating in the works of Gács and Harrington. Through numerical simulations, we obtain a fault-tolerant threshold for this code and hence provide strong evidence for the existence of fault-tolerant universal non-Abelian codes.