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Model-free quantum stabilisation via finite-difference Lyapunov control.

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Title: Model-free quantum stabilisation via finite-difference Lyapunov control.
Authors: Vrabel, Robert1 (AUTHOR) robert.vrabel@stuba.sk
Source: International Journal of Control. Jul2026, Vol. 99 Issue 7, p2168-2189. 22p.
Subjects: Lyapunov stability, Numerical differentiation, Stability (Mechanics), Qubits
Abstract: We develop a model-free framework for stabilising quantum states using only empirical finite-difference evaluations of a measurement-derived Lyapunov observable. The controller requires no knowledge of the Hamiltonian, dissipative structure, or generator of the dynamics, and relies solely on discrete measurement data. The approach combines three key elements: sign-based Lyapunov descent, adaptive gain amplification, and a finite-difference analogue of LaSalle's invariance principle. We provide rigorous conditions under which these mechanisms guarantee asymptotic stabilisation along the sampling instants in the drift-free case and practical input-to-state stability (ISS) in the presence of unknown drift and noise. The resulting feedback law is simple, derivative-free, and experimentally feasible. A qubit example illustrates the complete closed-loop scheme and the predicted ISS-type behaviour. Although demonstrated on a single qubit, the theory applies to arbitrary finite-dimensional quantum systems and offers a foundation for further developments in stochastic, subspace, and multi-qudit model-free quantum control. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Control is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Model-free quantum stabilisation via finite-difference Lyapunov control.
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  Data: We develop a model-free framework for stabilising quantum states using only empirical finite-difference evaluations of a measurement-derived Lyapunov observable. The controller requires no knowledge of the Hamiltonian, dissipative structure, or generator of the dynamics, and relies solely on discrete measurement data. The approach combines three key elements: sign-based Lyapunov descent, adaptive gain amplification, and a finite-difference analogue of LaSalle's invariance principle. We provide rigorous conditions under which these mechanisms guarantee asymptotic stabilisation along the sampling instants in the drift-free case and practical input-to-state stability (ISS) in the presence of unknown drift and noise. The resulting feedback law is simple, derivative-free, and experimentally feasible. A qubit example illustrates the complete closed-loop scheme and the predicted ISS-type behaviour. Although demonstrated on a single qubit, the theory applies to arbitrary finite-dimensional quantum systems and offers a foundation for further developments in stochastic, subspace, and multi-qudit model-free quantum control. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of International Journal of Control is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1080/00207179.2026.2656156
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      – Code: eng
        Text: English
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        PageCount: 22
        StartPage: 2168
    Subjects:
      – SubjectFull: Lyapunov stability
        Type: general
      – SubjectFull: Numerical differentiation
        Type: general
      – SubjectFull: Stability (Mechanics)
        Type: general
      – SubjectFull: Qubits
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      – TitleFull: Model-free quantum stabilisation via finite-difference Lyapunov control.
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              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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            – TitleFull: International Journal of Control
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