Quantum state transfer between twins in graphs

dc.contributor.authorMonterde, Hermie
dc.contributor.examiningcommitteePrymak, Andriy (Mathematics) Martin, Robert (Mathematics)en_US
dc.contributor.supervisorKirkland, Stephen (Mathematics) Plosker, Sarah (Mathematics and Computer Science, University of Brandon)en_US
dc.date.accessioned2021-09-09T19:31:58Z
dc.date.available2021-09-09T19:31:58Z
dc.date.copyright2021-08-26
dc.date.issued2021-08en_US
dc.date.submitted2021-08-26T20:05:56Zen_US
dc.degree.disciplineMathematicsen_US
dc.degree.levelMaster of Science (M.Sc.)en_US
dc.description.abstractA quantum spin network can be modelled by an undirected graph whose vertices and edges represent qubits and their interactions in the network, respectively. One major problem involving quantum spin networks is determining a time   such that the state at one vertex is transported to another vertex at time   with a particular level of probability, called the fidelity of quantum state transfer. Various useful types of quantum state transfer arise depending on the fidelity: periodicity, perfect state transfer, pretty good state transfer, and fractional revival. In this thesis, we investigate quantum state transfer between twin vertices in weighted graphs with or without loops. We provide spectral and algebraic characterizations of twin vertices, and use these to identify which properties of twin vertices are essential for various types of quantum state transfer to occur between any two of them. A characterization of vertices in unweighted graphs that exhibit strong cospectrality with an additional vertex in the post-twinning graph is also given. Moreover, we determine necessary and sufficient conditions for periodicity, perfect state transfer, pretty good state transfer, and fractional revival to occur between twin vertices with respect to adjacency dynamics. Then, we apply our results to double cones on regular graphs, which are a special class of graphs with twin vertices. Finally, we explore quantum state transfer in some common families of graphs with respect to adjacency dynamics.en_US
dc.description.noteMay 2021en_US
dc.identifier.urihttp://hdl.handle.net/1993/35937
dc.language.isoengen_US
dc.rightsopen accessen_US
dc.subjectTwin vertices, Quantum state transfer, Quantum walks, Twinningen_US
dc.titleQuantum state transfer between twins in graphsen_US
dc.typemaster thesisen_US
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