  Given the increasing use of shotcuts to adiabaticity (STA) to optimize power
and efficiency of quantum heat engines, it becomes a relevant question if there
are any theoretical limits to their application. We argue that quantum
fluctuations in the control device which implements the shortcut deflect the
system from the adiabatic path. This not only induces transitions to unwanted
final states but also changes the system energy, so that using the STA has a
definite cost in terms of conventional work definitions. This may be the
ultimate cost of an adiabatic shortcut, in the sense that it is present even
for a frictionless, zero temperature driving. We estimate the effect, to lowest
nontrivial order in the derivatives of the time-dependent frequency, on a
parametric harmonic oscillator, thus providing a consistency condition for the
validity of the classical approximation.
