Time-optimal generation of cluster states
Robert Fisher, Haidong Yuan, Andreas K. Spörl, Steffen J. Glaser · Physical Review A · 2009
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 $\frac{1}{2J}$. 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.