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International Conference on Electronics, Communications and Control

Quantum Optimal Control Based on the Constrained Control Field

Ze-Xia Huang, You-Hong Yu

Published Oct 16, 2012• 0 citations
Publisher

Abstract

According to the specialty of quantum systems, the reliability or the efficiency of a general optimal control scheme leave much to be desired. In this paper, we develop a special improved quantum optimal control method for using dynamic control field, which can be implemented as fast convergent algorithms. The relations among, convergence speed and iteration step parameters are analyzed in detail through a three-level ¦® system simulation experiments. Theoretical analysis show that this new algorithm exhibits significantly superior to the classical quantum optimal control method and the Krotov method in reliability and convergence rate.

DOI
10.1109/icecc.2012.631

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According to the specialty of quantum systems, the reliability or the efficiency of a general optimal control scheme leave much to be desired. In this paper, we develop a special improved quantum optimal control method for using dynamic control field, which can be implemented as fast convergent algorithms. The relations among, convergence speed and iteration step parameters are analyzed in detail through a three-level ¦® system simulation experiments. Theoretical analysis show that this new algorithm exhibits significantly superior to the classical quantum optimal control method and the Krotov method in reliability and convergence rate.
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One of the most popular methods for solving numerical optimal control problems is the Krotov method, adapted for quantum control by Tannor and coworkers. The Krotov method has the following three appealing properties: (1) monotonic increase of the objective with iteration number, (2) no requirement for a line search, leading to a significant savings over gradient (first-order) methods, and (3) macrosteps at each iteration, resulting in significantly faster growth of the objective at early iterations than in gradient methods where small steps are required. The principal drawback of the Krotov method is slow convergence at later iterations, which is particularly problematic when high fidelity is desired. We show here that, near convergence, the Krotov method degenerates to a first-order gradient method. We then present a variation on the Krotov method that has all the advantages of the original Krotov method but with significantly enhanced convergence (second-order or quasi-Newton) as the optimal solution is approached. We illustrate the method by controlling the three-dimensional dynamics of the valence electron in the Na atom.
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