  Adiabatic pulses are used extensively to enable robust control of quantum
operations. We introduce a new approach to adiabatic control that uses the
superadiabatic quality or $Q$-factor as a performance metric to design robust,
high fidelity pulses. This approach permits the systematic design of quantum
control schemes to maximize the adiabaticity of a unitary operation in a
particular time interval given the available control resources. The interplay
between adiabaticity, fidelity and robustness of the resulting pulses is
examined for the case of single-qubit inversion, and superadiabatic pulses are
demonstrated to have improved robustness to control errors. A numerical search
strategy is developed to find a broader class of adiabatic operations,
including multi-qubit adiabatic unitaries. We illustrate the utility of this
search strategy by designing control waveforms that adiabatically implement a
two-qubit entangling gate for a model NMR system.
