We present a network consisting of quantum gates that produces two imp
erfect copies of an arbitrary qubit. The quality of the copies does no
t depend on the input qubit. We also show that for a restricted class
of inputs it is possible to use a very similar network to produce thre
e copies instead of two. For qubits in this class, the copy quality is
again independent of the input and is the-same as the quality of the
copies produced by the two-copy network. [S1050-2947(97)09510-3].