Swinging small quantum systems out of available values of control parameters

When a quantum system is prepared in its many-body ground state, it can be adiabatically driven to another ground state by changing its control parameter. However, relying on adiabaticity is experimentally unjustified. Moreover, the target value of the control parameter may occur outside the experimentally accessible range. The indicated target state, however, can still be reached within a clever protocol of temporal changes of the control parameter provided its decomposition into some basis is known. It turns out that such a protocol can be obtained in the framework of the optimal control theory. In this paper, we show how to apply such an optimization scheme to small quantum systems treating interaction strength as the control parameter. We believe that the proposed approach can be creatively extended to various complex quantum systems.