  The optimal control of unitary transformations is a fundamental problem in
quantum control theory and quantum information processing. The feasibility of
performing such optimizations is determined by the computational and control
resources required, particularly for systems with large Hilbert spaces. Prior
work on unitary transformation control indicates that (i) for controllable
systems, local extrema in the search landscape for optimal control of quantum
gates have null measure, facilitating the convergence of local search
algorithms; but (ii) the required time for convergence to optimal controls can
scale exponentially with Hilbert space dimension. Depending on the control
system Hamiltonian, the landscape structure and scaling may vary. This work
introduces methods for quantifying Hamiltonian-dependent and kinematic effects
on control optimization dynamics in order to classify quantum systems according
to the search effort and control resources required to implement arbitrary
unitary transformations.
