Algebraic Graph Theory Seminar - Christopher van Bommel

Title: A Looped 4-Vertex Path Never Has Perfect State Transfer

Abstract:

A continuous quantum walk on a graph is determined by a
unitary matrix defined as a function of the adjacency matrix of the
graph.  A graph has perfect state transfer between two vertices if
there is a time at which the corresponding entry in the unitary matrix
has norm 1.  It is known that perfect state transfer does not occur
between the end-vertices of any path of length at least 4, however,
there is a claim based on numerical evidence that it can be achieved
for any length path by adding loops of an appropriate weight to the
end-vertices.  We will demonstrate that the claim is false for a
4-vertex path.