Designing a hybrid quantum controller for strongly eigenstate controllable systems

In this paper, a new quantum hybrid controller for controlling the strongly eigenstate controllable systems, is designed. For this purpose, a Lyapunov control law is implemented when the target state is in reachable set of the initial state. On the other hand, if the target state is not in the reachable set of the given initial state, based on Grover algorithm, a new interface state that the target state is in its reachable set,  will be found  and the given initial state is transferred to the new interface state. Then, the new interface state is transferred to the target state, based on a designed Lyapunov control law.  A new algorithm, for implementing the presented method, is designed. Finally, a simulated example illustrates the applications and advantages of presented method.