Multibit gates for quantum computing

We present a general technique to implement products of many qubit operator s communicating via a joint harmonic oscillator degree of freedom in a quan tum computer. By conditional displacements and rotations we can implement H amiltonians 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 algorith m can be implemented in a direct way.