ABSTRACT - DRUM - University of Maryland

dimensional non-chiral Majorana modes [47]. Just as the spinless p x + ip y superconductor
is the prototype of most two-dimensional non-Abelian superconductors,
its one-dimensional descendant, spinless fermions with p-wave pairing, can be considered
as the prototype model of all one-dimensional topological superconductors,
where Majorana zero-energy bound states are found at the ends of the topological
regions [28]. Similarly, one can realize one-dimensional p-wave superconductor in
semiconductor nanowire/superconductor heterostructures [59, 60]. An great advantage
of the one-dimensional realization is that the Zeeman field can be applied along
the wire, thus avoiding the destructive orbital effect without the need to introduce
the second interface to a ferromagnet.
The proposals have stimulated a burst of theoretical and experimental efforts
to design and engineer low-dimensional electronic systems that behaves like chiral
p x + ip y superconductors [61, 62, 63, 64]. Quite recently, the proposal involving
semiconductor nanowire/superconductor structure [59] has been claimed to be realized
in experiments and possible signatures of the desired Majorana zero modes
have been reported [65, 66, 67, 68].
1.6 Decoherence and Stability of Majorana Qubits
Ideally, a topological quantum computer based on non-Abelian anyons is free of
any errors and decoherence. This is because only the topological degrees of freedom
are used to build the quantum computer and non-topological degrees of freedom do
not participate in the low-energy physics. However, in reality this idealized scheme
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