  Adiabatic evolution is a powerful technique in quantum information and
computation. However, its performance is limited by the adiabatic theorem of
quantum mechanics. In this scenario, shortcuts to adiabaticity, such as
provided by the superadiabatic theory, constitute a valuable tool to speed up
the adiabatic quantum behavior. In this dissertation we introduce two different
models to perform universal superadiabatic quantum computing, which are based
on the use of shortcuts to adiabaticity by counter-diabatic Hamiltonians. The
first model is based on the use of superadiabatic quantum teleportation,
introduced in this dissertation, as a primitive to quantum computing. Thus, we
provide the counter-diabatic driving for arbitrary $n$-qubit gates. In
addition, our approach maps the counter-diabatic Hamiltonian for an arbitrary
$n$-qubit {\it gate} teleportation into the implementation of a rotated
counter-diabatic Hamiltonian for an $n$-qubit {\it state} teleportation. In the
second model we use the concept of controlled superadiabatic evolutions to show
how we can implement arbitrary $n$-controlled quantum gates. Remarkably, this
task can be performed by simple time-independent counter-diabatic Hamiltonians.
These two models can be used to design different sets of universal quantum
gates. We show that the use of the quantum speed limit suggests that the
superadiabatic time evolution is compatible with arbitrarily small time
intervals, where this arbitrariness is constrained to the energetic cost
necessary to perform the superadiabatic evolution.
