Implementation of a two-dimensional quantum walk using cross-Kerr nonlinearity

Abstract

A quantum walk is the quantum analog of the classical random walk, which provides a powerful tool for quantum computation and quantum simulation. However, the current experimental realization of the quantum walk based on photonic systems has been restricted to evolution in one dimension or small scale in two dimensions so far, and the growing demands cannot be fulfilled for further application of certain quantum computation tasks. Here, we theoretically propose a feasible scheme of a two-dimensional quantum walk with infinite steps by exploiting the orbital angular momentum of the photons and the phase information of the auxiliary coherent state induced by cross-Kerr nonlinearity. The numerical simulation shows that a proper parameter setting guarantees the walking for infinite steps in a two-dimensional grid with nearly $100\%$100% success probability.