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Izv. RAN. Ser. Mat., 2016, Volume 80, Issue 6, Pages 217–229 (Mi izv8567)  

This article is cited in 1 scientific paper (total in 1 paper)

On extrema of the objective functional for short-time generation of single-qubit quantum gates

A. N. Pechenab, N. B. Il'ina

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b National University of Science and Technology «MISIS»

Abstract: We study the extrema of the objective functional in the problem of generation of quantum gates (logical elements for quantum computations) for two-level systems with short duration of the control. We consider the problem of the existence of local but not global extrema, the so-called traps. The absence of traps was previously proved for a sufficiently long duration of the control. We prove that traps are absent for an arbitrarily small duration of the control for almost all target unitary operators and Hamiltonians. For the remaining target unitary operators and Hamiltonians we obtain a new lower bound for the duration of the control which guarantees the absence of traps.

Keywords: quantum control, qubit

DOI: https://doi.org/10.4213/im8567

Full text: PDF file (613 kB)
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English version:
Izvestiya: Mathematics, 2016, 80:6, 1200–1212

Bibliographic databases:

Document Type: Article
UDC: 517.977.5
PACS: 03.65.−w, 02.30.Yy, 32.80.Qk
MSC: 81Q93, 46N50
Received: 22.04.2016

Citation: A. N. Pechen, N. B. Il'in, “On extrema of the objective functional for short-time generation of single-qubit quantum gates”, Izv. RAN. Ser. Mat., 80:6 (2016), 217–229; Izv. Math., 80:6 (2016), 1200–1212

Citation in format AMSBIB
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\by A.~N.~Pechen, N.~B.~Il'in
\paper On extrema of the objective functional for short-time generation of single-qubit quantum gates
\jour Izv. RAN. Ser. Mat.
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\vol 80
\issue 6
\pages 217--229
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\crossref{https://doi.org/10.4213/im8567}
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\transl
\jour Izv. Math.
\yr 2016
\vol 80
\issue 6
\pages 1200--1212
\crossref{https://doi.org/10.1070/IM8567}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85011906808}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. B. Il'in, A. N. Pechen, “Conditions for the absence of local extrema in problems of quantum coherent control”, Proc. Steklov Inst. Math., 301 (2018), 109–113  mathnet  crossref  crossref  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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