  We propose deterministic realizations of nonlinear phase gates by repeating
non-commuting Rabi interactions feasible between a harmonic oscillator and {\em
only} a single two-level ancillary qubit. We show explicitly that the key
nonclassical features of the states after the ideal cubic phase gate and the
quartic phase gate are reproduced faithfully by the engineered operators. This
theoretical proposal completes the universal set of operators in continuous
variable quantum computation.
