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Near-time-optimal control for quantum systems

Author(s): Chen, Qi-Ming; Wu, Re-Bing; Zhang, Tian-Ming; Rabitz, Herschel

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Abstract: For a quantum system controlled by an external field, time-optimal control is referred to as the shortest-time-duration control that can still permit maximizing an objective function J, which is especially a desirable goal for engineering quantum dynamics against decoherence effects. However, since rigorously finding a time-optimal control is usually very difficult and in many circumstances the control is only required to be sufficiently short and precise, one can design algorithms seeking such suboptimal control solutions for much reduced computational effort. In this paper, we propose an iterative algorithm for finding near-time-optimal control in a high level set (i.e., the set of controls that achieves the same value of J) that can be arbitrarily close to the global optima. The algorithm proceeds seeking to decrease the time duration T while the value of J remains invariant, until J leaves the level-set value; the deviation of J due to numerical errors is corrected by gradient climbing that brings the search back to the level-set J value. Since the level set is very close to the maximum value of J, the resulting control solution is nearly time optimal with manageable precision. Numerical examples demonstrate the effectiveness and general applicability of the algorithm.
Publication Date: 16-Dec-2015
Citation: Chen, Qi-Ming, Wu, Re-Bing, Zhang, Tian-Ming, Rabitz, Herschel. (2015). Near-time-optimal control for quantum systems. PHYSICAL REVIEW A, 92 (10.1103/PhysRevA.92.063415
DOI: doi:10.1103/PhysRevA.92.063415
ISSN: 1050-2947
EISSN: 1094-1622
Pages: 063415-1 - 063415-7
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW A
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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