Majorana fermions, non-Abelian statistics, and topological quantum computation using semiconductors

Majorana fermions, particles which are their own antiparticles unlike
regular fermions, were envisioned by E. Majorana in 1935 to describe
neutrinos. A condensed matter realization of Majorana fermions is in
itself a remarkable phenomenon because of the fundamental new
properties of this (so far unrealized) particle. Recently there has
also been a resurgence of interest in Majorana fermions because of
their potential use in topological quantum computation (TQC), an idea
based on non-Abelian quantum statistics. We have made significant
progress in proposing a promising new condensed matter platform for
Majorana fermions, have analyzed its properties, and have proposed the
relevant TQC architectures. In this talk I will review the main
concepts of non-Abelian statistics, TQC, Majorana fermions, Majorana
based TQC, and our new proposal which may potentially lead to a
condensed matter realization of this exotic quantum particle.