  Quantum nonlinear operations for harmonic oscillator systems play a key role
in the development of analog quantum simulators and computers. Since a variety
of strong highly nonlinear operations are unavailable in the existing physical
systems, it is a common practice to approximate them by using conditional
measurement-induced methods. The conditional approach has several drawbacks,
the most severe of which is the exponentially decreasing success rate of the
strong and complex nonlinear operations. We show that by using a suitable two
level system sequentially interacting with the oscillator, it is possible to
resolve these issues and implement a nonlinear operation both nearly
deterministically and nearly perfectly. We explicitly demonstrate the approach
by constructing self-Kerr and cross-Kerr couplings in a realistic situation,
which require a feasible dispersive coupling between the two-level system and
the oscillator.
