  Fibonacci anyons are attractive for use in topological quantum computation
because any unitary transformation of their state space can be approximated
arbitrarily accurately by braiding. However there is no known braid that
entangles two qubits without leaving the space spanned by the two qubits. In
other words, there is no known "leakage-free" entangling gate made by braiding.
In this paper, we provide a remedy to this problem by supplementing braiding
with measurement operations in order to produce an exact controlled rotation
gate on two qubits.
