  A non-Hermitian shortcut to adiabaticity is introduced. By adding an
imaginary term in the diagonal elements of the Hamiltonian of a two state
quantum system, we show how one can cancel the nonadiabatic losses and perform
an arbitrarily fast population transfer, without the need to increase the
coupling. We apply this technique to two popular level-crossing models: the
Landau-Zener model and the Allen-Eberly model.
