Physics – Quantum Physics
Scientific paper
2010-08-30
J. Chem. Phys. 136, 104103 (2012)
Physics
Quantum Physics
Scientific paper
10.1063/1.3691827
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 Schr\"odinger 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.
Koch Christiane P.
Ndong Mamadou
Reich Daniel
No associations
LandOfFree
Monotonically convergent optimization in quantum control using Krotov's method does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Monotonically convergent optimization in quantum control using Krotov's method, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Monotonically convergent optimization in quantum control using Krotov's method will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-401142