Dissertation/Thesis Abstract

A Robust Protocol for Self-Testing Majorana Fermions
by Mayer, Karl, Ph.D., University of Colorado at Boulder, 2019, 101; 22587519
Abstract (Summary)

Majorana fermions arising in superconducting nanowires are of interest both for fundamental reasons and due to their potential use as building blocks for a topological quantum computer. While recent experiments have reported strong evidence of Majorana fermions in the form of occupation of a zero-energy fermionic mode, there is still disagreement about whether the observed data can be explained by other mechanisms. Furthermore, to be useful for quantum computation, the fermionic parities of zero-energy modes must be measured with high fidelity. In this thesis, we apply a quantum information protocol known as self-testing to a system of Majorana fermions. A self-testing protocol is a statistical test for certifying a quantum state and a set of measurement operators from experimentally determined expectation values, under minimal physical assumptions. Such a test treats the system as a black-box and relies only on the distributions of measurement outcomes given device settings. For the protocol described in this thesis, if the test is passed, then a set of measurements that ideally are of fermionic parities are certified to have the exact anticommutation relations as determined by the anticommutativity of Majorana fermion operators. The protocol is robust in the sense that bounds on the state and operator fidelities can still be established in the presence of small experimental imperfections. Finally, a rigorous statistical analysis is used to derive a confidence interval for the certified fidelities given a finite experimental data set.

Indexing (document details)
Advisor: Knill, Emanuel
Commitee: Smith, Graeme, Glancy, Scott
School: University of Colorado at Boulder
Department: Physics
School Location: United States -- Colorado
Source: DAI-B 81/3(E), Dissertation Abstracts International
Subjects: Physics, Quantum physics
Keywords: Self-testing Majorana fermions
Publication Number: 22587519
ISBN: 9781088349779
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