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Lorentz Transformation and Its Generalizations in Problems of Precisely Controlling the States of Multilevel Quantum Systems

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Abstract

A method of precision quantum measurements is proposed, which makes it possible to accurately track the states of multilevel quantum systems in Hilbert spaces of various dimensions. The developed quantum control algorithms are based on the use of the spinor representation of the Lorentz transformation group and its generalizations to the case of multilevel quantum systems. It is shown that feedback through weakly perturbing adaptive quantum measurements is capable of providing precise control of the quantum system, while introducing only weak perturbations in the initial quantum state.

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Funding

This work was supported by the Ministry of Science and Higher Education of the Russian Federation, program no. FFNN-2022-0016 for the Valiev Institute of Physics and Technology, Russian Academy of Sciences, by the Russian Foundation for Basic Research, grant no. 19-37-90109, and by the Foundation for the Advancement of Theoretical Physics and Mathematics BASIS, project no. 20-1-1-34-1.

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Authors and Affiliations

  1. Valiev Institute of Physics and Technology Institute, Russian Academy of Sciences, 117218, Moscow, Russia

    Yu. I. Bogdanov, N. A. Bogdanova, Yu. A. Kuznetsov & V. F. Lukichev

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  1. Yu. I. Bogdanov
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  2. N. A. Bogdanova
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  3. Yu. A. Kuznetsov
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  4. V. F. Lukichev
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Correspondence to Yu. I. Bogdanov.

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Bogdanov, Y.I., Bogdanova, N.A., Kuznetsov, Y.A. et al. Lorentz Transformation and Its Generalizations in Problems of Precisely Controlling the States of Multilevel Quantum Systems. Russ Microelectron 51, 43–53 (2022). https://doi.org/10.1134/S1063739722020044

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  • DOI: https://doi.org/10.1134/S1063739722020044

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