Date of Award


Document Type


Degree Name

Master of Science


Department of Engineering Physics

First Advisor

Michael V. Pak, PhD


A large barrier to practical quantum computation exists in the form of qubit decoherence, which leads to high noise and error when implementing quantum algorithms. A potential solution to this problem is the use of topologically-protected Majorana-based qubits, as their nonlocal nature and unique non-abelian exchange statistics render them virtually immune to decoherence while still allowing the state to be easily manipulated. For such a qubit to be constructed, it is essential to know the locations of the Majorana-hosting vortices in the system. This work presents a solution for the formation locations of vortices in a 2x2 superconducting island array, paving the way for the analysis of larger arrays that allow for the physical exchange of particles. Additionally, a method for determining the vortex locations in an irregularly-shaped Josephson junction is derived, allowing for accurate predictions of Majorana fermion locations in manufactured systems where the junctions may not be perfectly straight.

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