  The Heisenberg exchange interaction is a natural method to implement
non-local (i.e., multi-qubit) quantum gates in quantum information processing.
We consider quantum circuits comprising of $(SWAP)^\alpha $ gates, which are
realized through the exchange interaction, and single-qubit gates. A universal
two-qubit quantum circuit is constructed from only three $(SWAP)^\alpha$ gates
and six single-qubit gates. We further show that three $(SWAP)^\alpha $ gates
are not only sufficient, but necessary. Since six single-qubit gates are known
to be necessary, our universal two-qubit circuit is optimal in terms of the
number of {\em both} $(SWAP)^\alpha $ and single-qubit gates.
