  Starting with the basic control system model often employed in NMR pulse
design, we derive more realistic control system models taking into account
effects such as off-resonant excitation for systems with fixed inter-qubit
coupling controlled by globally applied electromagnetic fields, as well as for
systems controlled by a combination of a global fields and local control
electrodes. For both models optimal control is used to find controls that
implement a set of two- and three-qubit gates with fidelity greater than
99.99%. While in some cases the optimal pulses obtained appear to be
surprisingly simple and experimentally realistic, the results also show that
the "optimal" pulses obtained in other cases are experimentally infeasible, and
more sophisticated parametrization of the control fields and numerical
algorithms are needed.
