Quantum State Transfer On Q-graphs

Quantum state transfer of graph is a graph-theoretic problem derived from quantum computing theory.It has important applications in quantum information and quantum algorithm.In recent years,quantum state transfer of graph attracts widespread attention among computer science,physic and mathematics communities.In this thesis,we mainly focus on the problem of quantum state transfer of Q-graph.Our results can be divided into two parts.Part one,we mainly study perfect state transfer and pretty good state transfer on Q-graph.We show that if all eigenvalues of an r-regular graph G.r≥2,are integers,then its Q-graph,denoted by Q(G),has no perfect state transfer.Moreover,we exhibit a sufficient condition such that Q(G)has pretty good state transfer.Finally,applying the obtained results,we also exhibit many families of distance regular graphs,whose Q-graphs have no perfect state transfer,but admit pretty good state transfer.Part two,we mainly consider signless Laplacian perfect state transfer,signless Laplacian pretty good state transfer on Q-graph and how the operation of Q-graph affects quantum state transfer.We demonstrate that,for a regular graph G,if all the signless Laplacian eigenvalues are integers,then Q(G)has no signless Laplacian perfect state transfer.However,Q(G)admits signless Laplacian pretty good state transfer under some special restriction.In addition,in view of these results,we also present some families of Q-graphs,which have no signless Laplacian perfect state transfer,but admit signless Laplacian pretty good state transfer.