  We generalize the quantum adiabatic theorem to the non-Hermitian system and
build a rigorous adiabaticity condition with respect to the adiabatic phase.
The non-Hermitian Hamiltonian inverse engineering method is proposed for the
purpose to adiabatically drive a artificial quantum state. For the sake of
clearness, we take a concrete two-level system as an example to show the
usefulness of the inverse engineering method. The numerical simulation result
shows that our scheme can work well even under noise if the parameters are
chosen appropriately. We can obtain the desired target state by adjusting extra
rotating magnetic fields at a predefined time. Furthermore, certain noise and
dissipation in the systems is no longer undesirable, but plays a positive role
in our scheme. Therefore, our scheme could provide more choices for the
realization of quantum-state engineering.
