Optimizing the spatial spread of a quantum walk.

Abstract

We devise a protocol to build 1D time-dependent quantum walks in 1D maximizing the spatial spread throughout the procedure. We allow only one of the physical parameters of the coin-tossing operator to vary, i.e. the angle θ, such that for θ = 0 we have the ˆσz, while for θ = π/4 we obtain the Hadamard gate. The optimal θ sequences present non-trivial patterns, with mostly θ ≈ 0 alternated with θ ≈ π/4 values after increasingly long periods. We provide an analysis of the entanglement properties, quasi-energy spectrum and survival probability, providing a full physical picture.