  Quantum states with nonlinear squeezing are a necessary resource for
deterministic implementation of high-order quadrature phase gates that are, in
turn, sufficient for advanced quantum information processing. We demonstrate
that this class of states can be deterministically prepared by employing a
single Kerr gate accompanied by suitable Gaussian processing. The required Kerr
coupling depends on the energy of the initial system and can be made
arbitrarily small. We also employ numerical simulations to analyze the effects
of imperfections and to show to which extent can they be neglected.
