Optimal control landscape for the generation of unitary transformations with constrained dynamics

The reliable and precise generation of quantum unitary transformations is essential for the realization of a number of fundamental objectives, such as quantum control and quantum information processing. Prior work has explored the optimal control problem of generating such unitary transformations as a surface-optimization problem over the quantum control landscape, defined as a metric for realizing a desired unitary transformation as a function of the control variables. It was found that under the assumption of nondissipative and controllable dynamics, the landscape topology is trap free, which implies that any reasonable optimization heuristic should be able to identify globally optimal solutions. The present work is a control landscape analysis, which incorporates specific constraints in the Hamiltonian that correspond to certain dynamical symmetries in the underlying physical system. It is found that the presence of such symmetries does not destroy the trap-free topology. These findings expand the class of quantum dynamical systems on which control problems are intrinsically amenable to a solution by optimal control.