  We investigate the energetic advantage of accelerating a quantum harmonic
oscillator Otto engine by use of shortcuts to adiabaticity (for the expansion
and compression strokes) and to equilibrium (for the hot isochore), by means of
counter-diabatic (CD) driving. By comparing various protocols with and without
CD driving, we find that, applying both type of shortcuts leads to enhanced
power and efficiency even after the driving costs are taken into account. The
hybrid protocol not only retains its advantage in the limit cycle, but also
recovers engine functionality (i.e. a positive power output) in parameter
regimes where an uncontrolled, finite-time Otto cycle fails. We show that
controlling three strokes of the cycle leads to an overall improvement of the
performance metrics compared with controlling only the two adiabatic strokes.
Moreover, we numerically calculate the limit cycle behavior of the engine and
show that the engines with accelerated isochoric and adiabatic strokes display
a superior power output in this mode of operation.
