Quantum computation can be done by using non-abelian anyons which are neither bosons nor fermions. These exotic particles live only in two dimensional systems. Quasi-particles of = 5/2 fractional quantum Hall state will provide such non-abelian anyons. We discuss a NOT gate operation by braiding these anyons. In this work fundamental concepts of quantum computation are reviewed. Non-abelian anyons and topological phases are introduced. Some basic facts about fractional quantum Hall state are given. This is a book version of the MS thesis of the author."