  We introduce a shortcut to the adiabatic gate teleportation model of quantum
computation. More specifically, we determine fast local counterdiabatic
Hamiltonians able to implement teleportation as a universal computational
primitive. In this scenario, we provide the counterdiabatic driving for
arbitrary n-qubit gates, which allows to achieve universality through a variety
of gate sets. Remarkably, our approach maps the superadiabatic Hamiltonian for
an arbitrary n-qubit gate teleportation into the implementation of a rotated
superadiabatic dynamics of an n-qubit state teleportation. This result is
rather general, with the speed of the evolution only dictated by the quantum
speed limit. In particular, we analyze the energetic cost for different
Hamiltonian interpolations in the context of the energy-time complementarity.
