The continuous-time magnetic quantum walk and its probability invariance on a class of graphs.

Let L be a nonnegative integer and ΓL the power set of the set {0, 1,…,L}. Then there is an adjacency relation in ΓL such that ΓL together with the relation forms a regular graph. In this paper, we propose a model of continuous-time magnetic quantum walk (MQW) on the graph ΓL, and investigate its properties from a viewpoint of probability and quantum information. We first introduce a magnetic Laplacian ΔL(휃) on the graph ΓL and examine its spectrum. And then, with ΔL(휃) as the Hamiltonian, we construct our model of continuous-time MQW on the graph ΓL. We find that the model has probability distributions that are completely independent of the magnetic potential at all times. And we show that it has perfect state transfer at time t = π 2 when the magnetic potential satisfies some mild conditions. Some other interesting results are also obtained. [ABSTRACT FROM AUTHOR]