  Topological quantum computation is an implementation of a quantum computer in
a way that radically reduces decoherence. Topological qubits are encoded in the
topological evolution of two-dimensional quasi-particles called anyons and
universal set of quantum gates can be constructed by braiding these anyons
yielding to a topologically protected circuit model. In the present study we
remind the basics of this emerging quantum computation scheme and illustrate
how a topological qubit built with three Fibonacci anyons might be adopted to
achieve leakage free braiding gate by exchanging the anyons composing it. A
single-qubit braiding gate that approximates the Hadamard quantum gate to a
certain accuracy is numerically implemented using a brute force search method.
The algorithms utilized for that purpose are explained and the numerical
programs are publicly shared for reproduction and further use.
