  The reliable and precise generation of quantum unitary transformations is
essential to 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 non-dissipative and
controllable dynamics, the landscape topology is trap-free, implying that any
reasonable optimization heuristic should be able to identify globally optimal
solutions. The present work is a control landscape analysis incorporating
specific constraints in the Hamiltonian corresponding 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 solution by optimal control.
