  We present a general technique to implement products of many qubit operators
communicating via a joint harmonic oscillator degree of freedom in a quantum
computer. By conditional displacements and rotations we can implement
Hamiltonians which are trigonometric functions of qubit operators. With such
operators we can effectively implement higher order gates such as Toffoli gates
and C^n-NOT gates, and we show that the entire Grover search algorithm can be
implemented in a direct way.
