Quantum Walks on Oriented Graphs
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Date
2019-01-11
Authors
Lato, Sabrina
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
This thesis extends results about periodicity and perfect state transfer
to oriented graphs. We prove that if a vertex a is periodic, then elements of
the eigenvalue support lie in Z √∆ for some squarefree negative integer
∆. We find an infinite family of orientations of the complete graph that are
periodic. We find an example of a graph with both perfect state transfer
and periodicity that is not periodic at an integer multiple of the period, and
we prove and use Gelfond-Schneider Theorem to show that every oriented
graph with perfect state transfer between two vertices will have both vertices
periodic. We find a complete characterization of when perfect state transfer
can occur in oriented graphs, and find a new example of a graph where one
vertex has perfect state transfer to multiple other vertices.
Description
Keywords
quantum walks, graphs