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

Seeking the best control over a posed quantum dynamic objective\r\nentails climbing over the associated control landscape, which is defined\r\nas the quantum mechanical observable as a function of the controls. The\r\ntopology and general structure of quantum control landscapes as input „_\r\noutput maps dictate the final attainable yield, the efficiency of the\r\nsearch for an effective control, the possible existence of multiple\r\ndynamically equivalent controls, and the robustness of any viable control\r\nsolution. Normal optimization problems in virtually any area of\r\nengineering and science typically have landscape topologies that remain a\r\nmystery. Quantum mechanics appears to be quite special in that the\r\ntopology of quantum control landscapes can be established generically\r\nbased on minimal physical assumptions. Various features of these\r\nlandscapes will be discussed and illustrated for circumstances where the\r\ncontrols are either an external field or the time independent portions of\r\nthe Hamiltonian; the latter circumstance corresponds to subjecting the\r\nmaterial or molecules to systematic variation and hence viewed in the\r\ncontext of being controls. Both theoretical and experimental findings on\r\ncontrol landscapes and their consequences will be discussed, including\r\nissues of robustness to noise, search algorithm efficiency, existence of\r\nmultiple control solutions, simultaneous control of multiple quantum\r\nsystems (optimal dynamic discrimination (ODD)), and mechanism analysis. \r\nThe implications of this analysis for various application domains will be\r\ndiscussed.\r\n