Majorana fermions and its application on topological quantum computer

The majorana fermion represents a kind of particle which is its own antiparticle. This paper aims to analyze the majorana fermions from theoretical aspect and application aspect, including the derivation of Dirac equation and the practicality of topological quantum computer. This paper explores the idea of Majorana fermions from Dirac equation and the anyons which is an important quasi-particle to build a topological quantum computer. After that, the potentials of quantum computer are emphasized as well. Several current major difficulties faced by building a quantum computer have also been discussed, including the decoherence of qubit and the errors during the operation of qubit. The advantages of topological computer are mentioned as well, especially the high resistance to local perturbation. The important property of two-dimensional non-abelian anyons has been discussed as well. Finally, the important relation of majorana fermions with anyons are introduced and the reason why majorana fermions is important has also been revealed.