Quantum Walks on Oriented Graphs
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.
Collections
Cite this version of the work
Sabrina Lato
(2019).
Quantum Walks on Oriented Graphs. UWSpace.
http://hdl.handle.net/10012/14338
Other formats