Coherence evolution in two-dimensional quantum walk on lattice

Abstract

We investigate the evolution of the [Formula: see text] norm coherence in two-dimensional quantum walk on lattices for Fourier, Grover and Hadamard coins. Our study shows that the coherence of both the whole system and the position subsystem increases quadratically with the number of steps. We also analyze the influence of three kinds of noises, i.e. broken links, lattice congestion and lattice traps, on the two-dimensional quantum walk. The result shows that the increase of coherence with the number of steps gradually inclines to be linear as the probabilities of broken links and lattice congestion increase. In the quantum walk on trapped lattices, the coherence increases with the increasing time step before the crossover time [Formula: see text] and then gradually decreases after [Formula: see text].