  In many quantum technologies adiabatic processes are used for coherent
quantum state operations, offering inherent robustness to errors in the control
parameters. The main limitation is the long operation time resulting from the
requirement of adiabaticity. The superadiabatic method allows for faster
operation, by applying counterdiabatic driving that corrects for excitations
resulting from the violation of the adiabatic condition. In this article we
show how to construct the counterdiabatic Hamiltonian in a system with
forbidden transitions by using two-photon processes and how to correct for the
resulting time-dependent ac-Stark shifts in order to enable population transfer
with unit fidelity. We further demonstrate that superadiabatic stimulated Raman
passage can realize a robust unitary NOT-gate between the ground state and the
second excited state of a three-level system. The results can be readily
applied to a three-level transmon with the ladder energy level structure.
