The switching effect of the side chain on quantum walks on triple graphs

Abstract

We consider a continuous-time quantum walk on a triple graph and investigate the influence of the side chain on the propagation in the main chain. Calculating the interchange of the probabilities between the two parts of the main chain, we find that a switching effect appears if there are odd number of points on the side chain when concrete conditions between the length of the main chain and the position of the side chain are satisfied. Whereas, such an effect does not occur if there are even number of points on the side chain. We also suggest two proposals for experiment to observe such an effect, which may be employed to design new type of switching device.