  Ettore Majorana, in his short life, unintendedly has uncovered the most
profound problem in quantum computation by his discovery of Majorana fermion, a
particle which is its own anti-particle. Owing to its non-Abelian exchange
statistics, Majorana fermions may act as a qubit for a universal quantum
computer which is fault-tolerant. The existence of such particle is predicted
in mid-gap states (zero modes) of a topological superconductor as bound states
that have a highly entangled degenerate ground state. This introductory
overview will focus on the simplest theoretical proposals of Majorana fermions
for topological quantum computing in superconducting systems, emphasizing the
quest from the scalability problem of quantum computer to its possible solution
with topological quantum computer employing non-Abelian anyons on various
platforms of certain Majorana fermion signature encountered.
