Control of non-controllable quantum systems: A quantum control algorithm   based on Grover iteration
  A new notion of controllability, eigenstate controllability, is defined for finite-dimensional bilinear quantum mechanical systems which are neither strongly completely controllably nor completely controllable. And a quantum control algorithm based on Grover iteration is designed to perform a quantum control task of steering a system, which is eigenstate controllable but may not be (strongly) completely controllable, from an arbitrary state to a target state. 
Chen-Bin Zhang, Dao-Yi Dong, Zong-Hai Chen