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• W3104320935 endingPage "104103" @default.
• W3104320935 startingPage "104103" @default.
• W3104320935 abstract "The non-linear optimization method developed by Konnov and Krotov [Automation and Remote Control 60, 1427 (1999)] has been used previously to extend the capabilities of optimal control theory from the linear to the non-linear Schrodinger equation [Sklarz and Tannor, Phys. Rev. A 66, 053619 (2002)]. Here we show that based on the Konnov-Krotov method, monotonically convergent algorithms are obtained for a large class of quantum control problems. It includes, in addition to non-linear equations of motion, control problems that are characterized by non-unitary time evolution, non-linear dependencies of the Hamiltonian on the control, time-dependent targets and optimization functionals that depend to higher than second order on the time-evolving states. We furthermore show that the non-linear (second order) contribution can be estimated either analytically or numerically, yielding readily applicable optimization algorithms. We demonstrate monotonic convergence for an optimization functional that is an eighth-degree polynomial in the states. For the 'standard' quantum control problem of a convex final-time functional, linear equations of motion and linear dependency of the Hamiltonian on the field, the second-order contribution is not required for monotonic convergence but can be used to speed up convergence. We demonstrate this by comparing the performance of first and second order algorithms for two examples." @default.
• W3104320935 created "2020-11-23" @default.
• W3104320935 creator A5027928347 @default.
• W3104320935 creator A5067664592 @default.
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• W3104320935 date "2012-03-14" @default.
• W3104320935 modified "2023-10-13" @default.
• W3104320935 title "Monotonically convergent optimization in quantum control using Krotov's method" @default.
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• W3104320935 doi "https://doi.org/10.1063/1.3691827" @default.
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