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 numerical evidence that the nonlinear searching algorithm introduced by Wong and Meyer \mbox{%DIFAUXCMD meyer2013nonlinear , 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.