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Analysis and control of closed quantum systems based on real-valued dynamics

Analysis and control of closed quantum systems based on real-valued dynamics

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  • Author(s): Z. Xue 1 ; H. Lin 2 ; T.H. Lee 1, 3
    • View affiliations
    • Affiliations: 1: NUS Graduate School for Integrative Sciences and Technology, National University of Singapore, Singapore
      2: Department of Electrical Engineering, University of Notre Dame, Notre Dame, USA
      3: Department of Electrical and Computer Engineering, National University of Singapore, Singapore
  • Source: Volume 6, Issue 16, 1 November 2012, p. 2576 – 2584
    DOI:  10.1049/iet-cta.2011.0140 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Published

This study aims to facilitate quantum control design by making use of derived real-valued equations, which are equivalent to the Schrödinger equation. First, a pure-state identification approach is presented to show that a quantum state can be determined by a minimum number of real parameters. Second, the real-valued equations are deduced for both two- and three-level systems based on the results of the state parametrisation. The procedure is also extended to n-level systems. Third, with the assistance of the derived real-valued equations, the state transfer problem is investigated based on Lyapunov analysis. The state transfer convergence is analysed. It is further shown how to achieve arbitrary pure state transfers via the Lyapunov method by designing the control. The real-valued equations provide a convenient way for theoretical analysis and control design of quantum systems, and therefore can assist in the implementation of quantum control. The state transfer convergence is analysed. It is further shown how to achieve arbitrary pure-state transfers via the Lyapunov method by designing the control.

Inspec keywords: convergence of numerical methods; Lyapunov methods; discrete systems; control system synthesis; Schrodinger equation

Other keywords: real-valued dynamics; pure-state identification approach; real-valued equations; Lyapunov method; state parametrisation; two-level systems; Lyapunov analysis; real parameters; Schrodinger equation; quantum control design; pure-state transfer convergence; closed quantum system analysis; three-level systems; closed quantum system control

Subjects: Stability in control theory; Control system analysis and synthesis methods; Discrete control systems; Numerical analysis

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