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 Tr. Mat. Inst. Steklova, 2018, Volume 301, Pages 119–123 (Mi tm3900)

Conditions for the absence of local extrema in problems of quantum coherent control

N. B. Il'ina, A. N. Pechenab

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b National University of Science and Technology MISiS, Leninskii pr. 4, Moscow, 119049 Russia

Abstract: We consider a terminal control problem for quantum systems which is formulated as the problem of maximizing the objective functional at some fixed finite time. Within the framework of this problem, we discuss known results on the local maxima of the objective functional that are not global. This question is important for quantum control, since such local maxima could make it difficult to find the global maximum by local search in numerical optimization or under laboratory conditions.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 1.669.2016/1.4 The work was performed as a part of the project no. 1.669.2016/1.4.

DOI: https://doi.org/10.1134/S0371968518020097

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 301, 109–113

Bibliographic databases:

UDC: 517.977.5

Citation: N. B. Il'in, A. N. Pechen, “Conditions for the absence of local extrema in problems of quantum coherent control”, Complex analysis, mathematical physics, and applications, Collected papers, Tr. Mat. Inst. Steklova, 301, MAIK Nauka/Interperiodica, Moscow, 2018, 119–123; Proc. Steklov Inst. Math., 301 (2018), 109–113

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3900
• https://doi.org/10.1134/S0371968518020097
• http://mi.mathnet.ru/eng/tm/v301/p119

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This publication is cited in the following articles:
1. O. V. Morzhin, A. N. Pechen, “Krotov method for optimal control of closed quantum systems”, Russian Math. Surveys, 74:5 (2019), 851–908
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