Fractional scaling of quantum walks on two-dimensional percolation lattices

Abstract

We study the spreading behaviour of coined quantum walks on percolation lattices for both bond and site percolation on two‐dimensional Cartesian lattices. Using numerical simulation, we observe fractional scaling of the spreading with the number of steps of the walk. The exponent varies from zero at the critical percolation probability through to unity for the full lattice. For the lattices we simulate, up to 140×140, we observe faster than classical scaling for percolation probabilities above about 0.85.