  We study quantum information processing by means of optimal control theory.
To this end, we analyze the damped Jaynes-Cummings model, and derive optimal
control protocols that minimize the heating or energy dispersion rates, and
controls that drive the system at the quantum speed limit. Special emphasis is
put on analyzing the subtleties of optimal control theory for our system. In
particular, it is shown how two fundamentally different approaches to the
quantum speed limit can be reconciled by carefully formulating the problem.
