  We present numerical results which show how two-bit logic gates can be used
in the design of a quantum computer. We show that the Toffoli gate, which is a
universal gate for all classical reversible computation, can be implemented
using a particular sequence of exactly five two-bit gates. An arbitrary
three-bit unitary gate, which can be used to build up any arbitrary quantum
computation, can be implemented exactly with six two-bit gates. The ease of
implementation of any particular quantum operation is dependent upon a very
non-classical feature of the operation, its exact quantum phase factor.
