Trudy Matematicheskogo Instituta imeni V.A. Steklova
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Trudy Mat. Inst. Steklova, 2021, Volume 313, Pages 161–177 (Mi tm4173)  

On Reachable and Controllability Sets for Minimum-Time Control of an Open Two-Level Quantum System

Oleg V. Morzhin, Alexander N. Pechen

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: We consider a two-level open quantum system whose dynamics is governed by the Gorini–Kossakowski–Sudarshan–Lindblad equation with Hamiltonian and dissipation superoperator depending, respectively, on coherent and incoherent controls. Results about reachability, controllability, and minimum-time control are obtained in terms of the Bloch parametrization. First, we consider the case when the zero coherent and incoherent controls satisfy the Pontryagin maximum principle in the class of piecewise continuous controls. Second, for zero coherent control and for incoherent control lying in the class of constant functions, the reachability and controllability sets of the system are exactly described and some analytical results on the minimum-time control are found. Third, we consider a series of increasing values of the final time and the corresponding classes of controls with zero incoherent control and with coherent control equal to zero until a switching time instant and to a cosine function after it. The corresponding reachable points in the Bloch ball are numerically obtained and visualized. Fourth, a known method for estimating reachable sets is adapted and used to analyze the situation where the zero coherent and incoherent controls satisfy the Pontryagin maximum principle in the class of piecewise continuous controls while, as shown numerically, are not optimal.

Funding Agency Grant Number
Russian Science Foundation 17-11-01388
This work is supported by the Russian Science Foundation under grant 17-11-01388.


DOI: https://doi.org/10.4213/tm4173

Full text: PDF file (919 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2021, 313, 149–164

Bibliographic databases:

UDC: 517.977
Received: August 25, 2020
Revised: December 13, 2020
Accepted: December 26, 2020

Citation: Oleg V. Morzhin, Alexander N. Pechen, “On Reachable and Controllability Sets for Minimum-Time Control of an Open Two-Level Quantum System”, Mathematics of Quantum Technologies, Collected papers, Trudy Mat. Inst. Steklova, 313, Steklov Math. Inst., Moscow, 2021, 161–177; Proc. Steklov Inst. Math., 313 (2021), 149–164

Citation in format AMSBIB
\Bibitem{MorPec21}
\by Oleg~V.~Morzhin, Alexander~N.~Pechen
\paper On Reachable and Controllability Sets for Minimum-Time Control of an Open Two-Level Quantum System
\inbook Mathematics of Quantum Technologies
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 313
\pages 161--177
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4173}
\crossref{https://doi.org/10.4213/tm4173}
\elib{https://elibrary.ru/item.asp?id=46929717}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 313
\pages 149--164
\crossref{https://doi.org/10.1134/S0081543821020152}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000674956500015}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85109405914}


Linking options:
  • http://mi.mathnet.ru/eng/tm4173
  • https://doi.org/10.4213/tm4173
  • http://mi.mathnet.ru/eng/tm/v313/p161

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:203
    References:7
    First page:9

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021