Topological quantum computing is an alternative framework for avoiding thequantum decoherence problem in quantum computation. The problem of executing agate 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 optimalproduct of braid generators where the optimality is defined in terms of thegate approximation and the braid's length. In this paper we propose the use ofdifferent variants of estimation of distribution algorithms to deal with theproblem. Furthermore, we investigate how the regularities of the braidoptimization problem can be translated into statistical regularities by meansof the Boltzmann distribution. We show that our best algorithm is able toproduce many solutions that approximates the target gate with an accuracy inthe order of $10^{-6}$, and have lengths up to 9 times shorter than thoseexpected from braids of the same accuracy obtained with other methods.
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