  In this article we use optimal control to maximize the efficiency of a
quantum heat engine executing the Otto cycle in the presence of external noise.
We optimize the engine performance for both amplitude and phase noise. In the
case of phase damping we additionally show that the ideal performance of a
noiseless engine can be retrieved in the adiabatic (long time) limit. The
results obtained here are useful in the quest for absolute zero, the design of
quantum refrigerators that can cool a physical system to the lowest possible
temperature. They can also be applied to the optimal control of a collection of
classical harmonic oscillators sharing the same time-dependent frequency and
subjected to similar noise mechanisms. Finally, our methodology can be used for
the optimization of other interesting thermodynamic processes.
