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Pareto-front shape in multiobservable quantum control

Author(s): Sun, Qiuyang; Wu, Re-Bing; Rabitz, Herschel

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Abstract: Many scenarios in the sciences and engineering require simultaneous optimization of multiple objective functions, which are usually conflicting or competing. In such problems the Pareto front, where none of the individual objectives can be further improved without degrading some others, shows the tradeoff relations between the competing objectives. This paper analyzes the Pareto-front shape for the problem of quantum multiobservable control, i.e., optimizing the expectation values of multiple observables in the same quantum system. Analytic and numerical results demonstrate that with two commuting observables the Pareto front is a convex polygon consisting of flat segments only, while with noncommuting observables the Pareto front includes convexly curved segments. We also assess the capability of a weighted-sum method to continuously capture the points along the Pareto front. Illustrative examples with realistic physical conditions are presented, including NMR control experiments on a 1 H − 13 C two-spin system with two commuting or noncommuting observables.
Publication Date: 17-Mar-2017
Citation: Sun, Qiuyang, Wu, Re-Bing, Rabitz, Herschel. (2017). Pareto-front shape in multiobservable quantum control. Physical Review A, 95 (3), 10.1103/PhysRevA.95.032319
DOI: doi:10.1103/PhysRevA.95.032319
ISSN: 2469-9926
EISSN: 2469-9934
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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