Implementing arbitrary coined two-dimensional quantum walks via bulk optical interferometry

Multi-dimensional quantum walks provide a powerful tool for simulating quantum phenomena. We design a feasible scheme to implement two-dimensional quantum walks in a “real” position space, demonstrating a scalable quantum walk on a non-trivial graph structure with single photons and bulk optical interferometry. By combining the spatial modes and polarizations of photons, we expand the dimensions of the coin states from two to four and implement arbitrary four-side coin flipping. Furthermore, with the growth of the number of walk steps, the number of linear optical elements increases linearly. This significantly reduces the resources necessary for its feasible experimental realization. Our scheme is then remarkably scalable and feasible with current technologies. Our results illustrate the potential of a two-dimensional quantum walk as a route for simulating and understanding complex quantum systems.