  Topological quantum computing is an alternative framework for avoiding the
quantum decoherence problem in quantum computation. The problem of executing a
gate in this framework can be posed as the problem of braiding quasiparticles.
Because these are not Abelian, the problem can be reduced to finding an optimal
product of braid generators where the optimality is defined in terms of the
gate approximation and the braid's length. In this paper we propose the use of
different variants of estimation of distribution algorithms to deal with the
problem. Furthermore, we investigate how the regularities of the braid
optimization problem can be translated into statistical regularities by means
of the Boltzmann distribution. We show that our best algorithm is able to
produce many solutions that approximates the target gate with an accuracy in
the order of $10^{-6}$, and have lengths up to 9 times shorter than those
expected from braids of the same accuracy obtained with other methods.
