ABSTRACT - DRUM - University of Maryland

We also notice that in this formulation, the Abelian phase in the braiding is totally
out of reach. It is very likely that occupations of the midgap states cause dephasing
of this Abelian phase.
This result is thoroughly non-obvious because it may appear on first sight
that arbitrary thermal occupancies of the mid-gap excited states would completely
suppress the non-Abelian nature of the system since the Majorana mode resides
entirely at zero energy and not in the excited mid-gap states.
We now briefly discuss how the condition of fermion parity conservation are
satisfied in realistic systems. It requires that no local physical processes that can
change fermion parity are present in the system. This is indeed the case in a superconductor
since the presence of bulk superconducting gap suppresses single-particle
excitations at low energies and results in even-odd effect in fermion number. Therefore
in a fully gapped superconductor the fermion parity is indeed well-defined at
equilibrium and there are no parity-violation processes intrinsic to the superconductor.
On the other hand, if the topological qubits are in contact with gapless
fermions, the fermion parity is apparently not a good quantum number (see [107]
for a detailed discussion of related issues and possible resolutions). Therefore the
topological qubits have to be separated galvanically from external sources of unpaired
electrons, which can also be achieved experimentally(e.g. in superconducting
charge qubits [114]).
83