  Achieving effectively adiabatic dynamics is a ubiquitous goal in almost all
areas of quantum physics. Here, we study the speed with which a quantum system
can be driven when employing transitionless quantum driving. As a main result,
we establish a rigorous link between this speed, the quantum speed limit, and
the (energetic) cost of implementing such a shortcut to adiabaticity.
Interestingly, this link elucidates a trade-off between speed and cost, namely
that instantaneous manipulation is impossible as it requires an infinite cost.
These findings are illustrated for two experimentally relevant systems - the
parametric oscillator and the Landau-Zener model - which reveal that the
spectral gap governs the quantum speed limit as well as the cost for realizing
the shortcut.
