Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 57, Issue 8, Pages 2021-2032Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2012.2195920
Keywords
Convergence of numerical methods; optimal control; robust control
Funding
- National Science Foundation [0747877]
- Air Force Office of Scientific Research [FA9550-10-1-0146]
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [0747877] Funding Source: National Science Foundation
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Inhomogeneity, in its many forms, appears frequently in practical physical systems. Readily apparent in quantum systems, inhomogeneity is caused by hardware imperfections, measurement inaccuracies, and environmental variations, and subsequently limits the performance and efficiency achievable in current experiments. In this paper, we provide a systematic methodology to mathematically characterize and optimally manipulate inhomogeneous ensembles with concepts taken from ensemble control. In particular, we develop a computational method to solve practical quantum pulse design problems cast as optimal ensemble control problems, based on multidimensional pseudospectral approximations. We motivate the utility of this method by designing pulses for both standard and novel applications. We also show the convergence of the pseudospectral method for optimal ensemble control. The concepts developed here are applicable beyond quantum control, such as to neuron systems, and furthermore to systems with by parameter uncertainty, which pervade all areas of science and engineering.
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