  We discuss the energetic cost of superadiabatic models of quantum
computation. Specifically, we investigate the energy-time complementarity in
general transitionless controlled evolutions and in shortcuts to the adiabatic
quantum search over an unstructured list. We show that the additional energy
resources required by superadiabaticity for arbitrary controlled evolutions can
be minimized by using probabilistic dynamics, so that the optimal success
probability is fixed by the choice of the evolution time. In the case of analog
quantum search, we show that the superadiabatic approach induces a non-oracular
counter-diabatic Hamiltonian, with the same energy-time complexity as
equivalent adiabatic implementations.
