Before revision: We provide first evidence that some families of nonlinear quantum systems , rephrased in terms of coined quantum walks with effective nonlinear phase, display a strong computational advantage for search algorithms, over graphs having sets of vertices of constant size, e. g. the infinite square grid.
After revision: We provide first evidence that some families of nonlinear quantum systems , rephrased in terms of coined quantum walks with effective nonlinear phase, can be extended to the finite 2-dimensional grid, keeping the same computational advantage