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Exploiting multi-dimensional quantum walks as feasible platforms for quantumcomputation and quantum simulation is attracting constantly growing attentionfrom a broad experimental physics community. Here, we propose a two-dimensionalquantum walk scheme with a single-qubit coin that presents, in the consideredregimes, a strong localization-like effect on the walker. The result couldprovide new possible directions for the implementation of quantum algorithms orfrom the point of view of quantum simulation. We characterize thelocalization-like effect in terms of the parameters of a step-dependent qubitoperation that acts on the coin space after any standard coin operation,showing that a proper choice can guarantee a non-negligible probability offinding the walker in the origin even for large times. We finally discuss therobustness to imperfections, a qualitative relation with coherences behavior,and possible experimental realizations of this model with the currentstate-of-the-art settings.

Localization-like effect in two-dimensional alternate quantum walks with periodic coin operations