  The definition of a cluster state naturally suggests an implementation
scheme: find a physical system with an Ising coupling topology identical to
that of the target state, and evolve freely for a time of 1/2J. Using the tools
of optimal control theory, we address the question of whether or not this
implementation is time-optimal. We present some examples where it is not and
provide an explanation in terms of geodesics on the Bloch-sphere.
