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Tr. Mat. Inst. Steklova, 2014, Volume 285, Pages 244–252 (Mi tm3552)  

This article is cited in 7 scientific papers (total in 7 papers)

Coherent control of a qubit is trap-free

A. N. Pechen, N. B. Il'in

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: There is a strong interest in optimal manipulating of quantum systems by external controls. Traps are controls which are optimal only locally but not globally. If they exist, they can be serious obstacles to the search of globally optimal controls in numerical and laboratory experiments, and for this reason the analysis of traps attracts considerable attention. In this paper we prove that for a wide range of control problems for two-level quantum systems all locally optimal controls are also globally optimal. Hence we conclude that two-level systems in general are trap-free. In particular, manipulating qubits – two-level quantum systems forming a basic building block for quantum computation – is free of traps for fundamental problems such as the state preparation and gate generation.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-31115
This work was supported by the Russian Foundation for Basic Research, project no. 14-01-31115.


DOI: https://doi.org/10.1134/S0371968514020162

Full text: PDF file (189 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 285, 233–240

Bibliographic databases:

Document Type: Article
UDC: 517.977.5
Received in January 2014

Citation: A. N. Pechen, N. B. Il'in, “Coherent control of a qubit is trap-free”, Selected topics of mathematical physics and analysis, Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth, Tr. Mat. Inst. Steklova, 285, MAIK Nauka/Interperiodica, Moscow, 2014, 244–252; Proc. Steklov Inst. Math., 285 (2014), 233–240

Citation in format AMSBIB
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\publ MAIK Nauka/Interperiodica
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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. A. N. Pechen, N. B. Il'in, “Existence of traps in the problem of maximizing quantum observable averages for a qubit at short times”, Proc. Steklov Inst. Math., 289 (2015), 213–220  mathnet  crossref  crossref  isi  elib
    2. A. N. Pechen, N. B. Il'in, “On critical points of the objective functional for maximization of qubit observables”, Russian Math. Surveys, 70:4 (2015), 782–784  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. N. Pechen, “On the speed gradient method for generating unitary quantum operations for closed quantum systems”, Russian Math. Surveys, 71:3 (2016), 597–599  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Alexander N. Pechen, Nikolay B. Il'in, “On the problem of maximizing the transition probability in an $n$-level quantum system using nonselective measurements”, Proc. Steklov Inst. Math., 294 (2016), 233–240  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. A. N. Pechen, N. B. Il'in, “On extrema of the objective functional for short-time generation of single-qubit quantum gates”, Izv. Math., 80:6 (2016), 1200–1212  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. A. N. Pechen, N. B. Il'in, “Control landscape for ultrafast manipulation by a qubit”, J. Phys. A-Math. Theor., 50:7 (2017), 075301  crossref  mathscinet  zmath  isi  scopus
    7. 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
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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