  This work studies the feasibility of optimal control of high-fidelity quantum
gates in a model of interacting two-level particles. One particle (the qubit)
serves as the quantum information processor, whose evolution is controlled by a
time-dependent external field. The other particles are not directly controlled
and serve as an effective environment, coupling to which is the source of
decoherence. The control objective is to generate target one-qubit gates in the
presence of strong environmentally-induced decoherence and under physically
motivated restrictions on the control field. It is found that interactions
among the environmental particles have a negligible effect on the gate fidelity
and require no additional adjustment of the control field. Another interesting
result is that optimally controlled quantum gates are remarkably robust to
random variations in qubit-environment and inter-environment coupling
strengths. These findings demonstrate the utility of optimal control for
management of quantum-information systems in a very precise and specific
manner, especially when the dynamics complexity is exacerbated by inherently
uncertain environmental coupling.
