**Hiking over quantum control landscapes (MITACS QIP Seminar Series)** - Herschel Rabitz

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.