From Majorana fermions to topological quantum computation

Abstract

In 1937, Majorana solved the relativistic wave equation for electrons proposed by Dirac in a different representation, deriving a brand new solution describing a kind of neutral fermions without any chargers which is called Majorana fermions that show completely different properties from Dirac fermions. In the field of condensed matter physics, it is clear that there are certain kinds of quasiparticles which have similar behaviors to Majorana fermions in the searches of topological superconductors and fractional quantum Hall effects. Especially, zero-energy Majorana fermion modes in two-dimensional topological superconductors show non-abelian anyonic statistical properties under exchange operations, which can realize the so-called topological quantum computation that is fault-tolerant on the hardware level. In this article the history and then introduce latest progress of Majorana fermions will be reviewed. On the basis of above information, there is a brief discussion on present situations and prospects of the topological quantum computation with the importance of Majorana fermions.