  We present a general, systematic, and efficient method for decomposing any
given exponential operator of bosonic mode operators, describing an arbitrary
multi-mode Hamiltonian evolution, into a set of universal unitary gates.
Although our approach is mainly oriented towards continuous-variable quantum
computation, it may be used more generally whenever quantum states are to be
transformed deterministically, e.g. in quantum control, discrete-variable
quantum computation, or Hamiltonian simulation. We illustrate our scheme by
presenting decompositions for various nonlinear Hamiltonians including quartic
Kerr interactions. Finally, we conclude with two potential experiments
utilizing offline-prepared optical cubic states and homodyne detections, in
which quantum information is processed optically or in an atomic memory using
quadratic light-atom interactions.
