ABSTRACT - DRUM - University of Maryland

effect of quasiparticle tunneling on the topological degeneracy that is fundamental
to the realization of topological qubits, and calculated the energy splitting of the
degenerate states using a generalized WKB method. We found the energy splitting
exhibits an oscillatory behavior with the inter-vortex distance, apart from the
well-known exponential suppression. The presence of these oscillations has important
implications for topological quantum computation, since the energy splitting
determines the fusion channel of two non-Abelian vortices. In Chapter 5 we turn
to the question of thermal effects on the topological quantum computation scheme
based on Majorana quasiparticles. We distinguished two types of fermionic excitations
that can possibly spoil the topological protection of qubits, the localized
midgap states and extended states above the gap, and considered their effects on
the braiding, read out and the lifetime of the qubits. We exploited a density matrix
formulation based on physical observables and found the topological braiding
remains intact in the presence of thermal excitations. However, thermally excited
midgap states do result in decoherence in the read out of topological qubits based
on vortex interferometry and we derived an analytical expression for the deduction
in the interference visibility using a simplified but still physical model. In Chapter 6
we consider the effect of non-adiabaticity on vortex braiding in a microscopic model
of a spinless p x + ip y superconductor. We developed a time-dependent Bogoliubovde
Gennes equation approach to describe time evolution of BCS superconductors.
With the help of this formalism, we studied the robustness of the braiding operations
when non-adibaticity is taken into account and calculated the corrections to
the Ivanov’s rule perturbatively. In Chapter 7, we addressed the question of whether
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