Finite-time stabilization of stochastic spin-[Formula presented] system via strict Lyapunov control

Abstract

Finite-time stabilization of open quantum systems is essential for advancing time-critical applications in quantum computing, communication, and metrology. This paper addresses the problem of stabilizing a two-level open quantum system — modeled by the quantum stochastic master equation (SME) — to a target eigenstate within a finite time. We develop a continuous-time measurement-based feedback control strategy rooted in strict Lyapunov theory, which ensures practical finite-time convergence of the system state in the mean-square sense. The control law is explicitly constructed as a nonlinear state-feedback function of the density matrix, and we derive sufficient conditions for finite-time convergence using Lyapunov bounds. Furthermore, we show that when these conditions are relaxed, the same control law yields exponential stability. The proposed method also provides an explicit settling-time function that quantifies the time to convergence in terms of initial conditions and system parameters. Numerical simulations validate the theoretical results and demonstrate the effectiveness of the proposed approach compared to exponential stabilization method. © 2025 The Authors