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Adiabatic state engineering is a powerful technique in quantum informationand quantum control. However, its performance is limited by the adiabatictheorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, suchas provided by the superadiabatic theory, constitute a valuable tool to speedup the adiabatic quantum behavior. Here, we propose a superadiabatic route toimplement universal quantum computation. Our method is based on the realizationof piecewise controlled superadiabatic evolutions. Remarkably, they can beobtained by simple time-independent counter-diabatic Hamiltonians. Inparticular, we discuss the implementation of fast rotation gates and arbitraryn-qubit controlled gates, which can be used to design different sets ofuniversal quantum gates. Concerning the energy cost of the superadiabaticimplementation, we show that it is dictated by the quantum speed limit,providing an upper bound for the corresponding adiabatic counterparts.

Superadiabatic Controlled Evolutions and Universal Quantum Computation