A quantum gate is a special unitary matrix used to evolve from a superposition of states to another superposition of states during a quantum computation. A Theorem by two mathematicians, Jean-Luc Brylinski and Ranee Brylinski, asserts that in order to be able to approximate any quantum gate of n qudits that is an element of SU(d^n) -- in quantum computing language this is called "universal quantum computation" -- it is sufficient to be able to approximate any 1-qudit gate and have just one 2-qudit entangling gate. In this talk d=3, namely we deal with qutrits. We investigate the second point of the Brylinski theorem and show how to physically realize a 2-qutrit entangling gate by moving particles around called anyons.