Journal of Automation and Intelligence (Dec 2022)

Lyapunov-based fixed-time stabilization control of quantum systems

  • Xiaolei Li,
  • Changyun Wen,
  • Jiange Wang

Journal volume & issue
Vol. 1, no. 1
p. 100005

Abstract

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In this paper, we consider the fixed-time stabilization control problem of quantum systems modeled by Schrödinger equations. Firstly, the Lyapunov-based fixed-time stability criterion is extended to finite-dimensional closed quantum systems in the form of coherence vectors. Then for a two-level quantum system with single control input, a non-smooth fractional-order control law is designed using the relative state distance. By integrating the fixed-time Lyapunov control technique and the bi-limit homogeneity theory, the quantum system is proved to be stabilized to an eigenstate of the inherent Hamiltonian in a fixed time. Comparing with existing methods in quantum system control, the proposed approach can guarantee stabilization in a fixed time without depending on the initial states.

Keywords