Quantum Walks on Oriented Graphs

quantum walks;graphs

Lato, Sabrinaadvisor:Godsil, Chris ; affiliation1:Faculty of Mathematics ; Godsil, Chris ;

University of Waterloo

关键词: quantum walks;    graphs;    Master Thesis;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/14338/3/Lato_Sabrina.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

This thesis extends results about periodicity and perfect state transferto oriented graphs. We prove that if a vertex a is periodic, then elements ofthe eigenvalue support lie in Z √∆ for some squarefree negative integer∆. We find an infinite family of orientations of the complete graph that areperiodic. We find an example of a graph with both perfect state transferand periodicity that is not periodic at an integer multiple of the period, andwe prove and use Gelfond-Schneider Theorem to show that every orientedgraph with perfect state transfer between two vertices will have both verticesperiodic. We find a complete characterization of when perfect state transfercan occur in oriented graphs, and find a new example of a graph where onevertex has perfect state transfer to multiple other vertices.