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Controllability of Quantum Systems with SU(1, 1) Dynamical Symmetry

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Abstract

This paper presents sufficient and necessary conditions for the propagator controllability of a class of infinite-dimensional quantum systems with SU(1, 1) dynamical symmetry through the isomorphic mapping to the non-unitary representation of SU(1, 1). We prove that the elliptic condition of the total Hamiltonian is both necessary and sufficient for the controllability and strong controllability. The obtained results can be also extended to control systems with SO(2, 1) dynamical symmetry.

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Authors and Affiliations

  1. Beijing Aerospace Automatic Control Institute, Beijing, 100854, China

    Jianwu Wu

  2. Department of Automation, Tsinghua University, Beijing, 100084, China

    Rebing Wu, Jing Zhang & Chunwen Li

  3. Center for Quantum Information Science and Technology, BNRist, Beijing, 100084, China

    Rebing Wu, Jing Zhang & Chunwen Li

Authors
  1. Jianwu Wu
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  2. Rebing Wu
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  3. Jing Zhang
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  4. Chunwen Li
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Corresponding authors

Correspondence to Jianwu Wu, Rebing Wu, Jing Zhang or Chunwen Li.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 61803357, 61833010, 61773232, 61622306 and 11674194, the National Key R&D Program of China under Grant Nos. 2018YFA0306703 and 2017YFA0304304, the Tsinghua University Initiative Scientific Research Program, and the Tsinghua National Laboratory for Information Science and Technology Cross-discipline Foundation.

This paper was recommended for publication by Editor SUN Jian.

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Wu, J., Wu, R., Zhang, J. et al. Controllability of Quantum Systems with SU(1, 1) Dynamical Symmetry. J Syst Sci Complex 34, 827–842 (2021). https://doi.org/10.1007/s11424-020-9259-9

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  • DOI: https://doi.org/10.1007/s11424-020-9259-9

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