Date of Award

3-2021

Document Type

Thesis

Degree Name

Master of Science in Applied Physics

Department

Department of Engineering Physics

First Advisor

Michael M. Pak, PhD

Abstract

Topological systems are immune to decoherence and provide a hunting ground for qubits that are fault tolerant. The process of calculating linear operator representations of Majorana fermion exchanges or braids is well known and well documented; however, there is no documented intuition or algorithm which provides the opposite; braids from quantum gates. In this document, all possible linear representations of single, double, triple, and quadruple qubit gates are calculated to find several key patterns which provide crucial insight into the manifestation of qubit gates. A n x n gate will require n + 2 Majoranas with ½n + 1 trivial braids and ½n coupling braids possible. The native gates produced are either tensor products or tensor sums of the well known phase gate and Pauli X gate, demonstrating that a topological SC Majoranas qubit may only explore the poles of the Bloch sphere. Additionally, the exact compact forms of all possible gates are listed. These insights are an important step to forming a complete understanding of the braids' effects on the multi qubit system which is necessary if one is to take advantage of this fault tolerant method of quantum computation.

AFIT Designator

AFIT-ENP-MS-21-M-134

DTIC Accession Number

AD1145742

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