Seeking the best control over a posed quantum dynamic objective entails
climbing over the associated control landscape, which is defined as the
quantum mechanical observable as a function of the controls. The
topology and general structure of quantum control landscapes as input
& output maps dictate the final attainable yield, the
efficiency of the search for an effective control, the possible
existence of multiple dynamically equivalent controls, and the
robustness of any viable control solution. Normal optimization problems
in virtually any area of engineering and science typically have
landscape topologies that remain a mystery. Quantum mechanics appears
to be quite special in that the topology of quantum control landscapes
can be established generically based on minimal physical assumptions.
Various features of these landscapes will be discussed and illustrated
for circumstances where the controls are either an external field or the
time independent portions of the Hamiltonian; the latter circumstance
corresponds to subjecting the material or molecules to systematic
variation and hence viewed in the context of being controls. Both
theoretical and experimental findings on control landscapes and their
consequences will be discussed, including issues of robustness to noise,
search algorithm efficiency, existence of multiple control solutions,
simultaneous control of multiple quantum systems (optimal dynamic
discrimination (ODD)), and mechanism analysis. The implications of this
analysis for various application domains will be discussed.
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