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International Conference on Control and Automation

Global stabilization of an eigenstate for stochastic quantum systems

Shuang Cong, Jie Wen, Sen Kuang, Fangfang Meng

Published Jun 1, 2016• 3 citations
Publisher

Abstract

The global stabilization of an eigenstate for finite dimensional stochastic quantum systems with non-diagonal free Hamiltonian and non-regular measurement operator is studied in this paper. A two-part switching control strategy is proposed, in which a constant control is used to steer the system state to enter the convergence domain; another control law, which is designed based on Lyapunov stability theorem is used to attract the system state in convergence domain to the target state. The convergence of the target eigenstate from an arbitrary initial state is strictly proved. Moreover, the numerical experiments on a three dimensional stochastic quantum system are implemented to demonstrate the effectiveness of the control proposed.

DOI
10.1109/icca.2016.7505405

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The global stabilization of mixed states for finite dimensional stochastic quantum systems with non-regular measurement operator and non-diagonal free Hamiltonian is investigated in this paper. A two-part switching control strategy is proposed, in which the constant control is used to steer the system state to enter the convergence domain, while the control law which is designed based on Lyapunov stability theorem is used to attract the system state in convergence domain to the target state. The convergence of the switching control is strictly proved. Moreover, the numerical experiments on a three dimensional stochastic quantum system are implemented to demonstrate the effectiveness of the control proposed.
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We propose a new method for pure-state and subspace preparation in quantum systems, which employs the output of a continuous measurement process and switching dissipative control to improve convergence speed, as well as robustness with respect to the initial conditions. In particular, we prove that the proposed closed-loop strategy makes the desired target globally asymptotically stable both in mean and almost surely, and we show it compares favorably against a time-based and a state-based switching control law, with significant improvements in the case of faulty initialization.
We propose a Lyapunov-based control method for stochastic quantum systems. The method can make the quantum state converge to a separable mixed target state from an arbitrary initial state. Specifically, the target state can be written as the tensor product of two matrices. Based on a well designed virtual mechanical quantity, a Lyapunov function and two control laws are presented: one can make the system equilibria in the largest invariant set stable according to LaSalle's invariance principle, and the other one can make the target state globally asymptotically stable.
This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian measurement operator of a two-level quantum system. In open loop, such system converges stochastically to one of the eigenstates of the measurement operator. Previous work has proposed state feedback that destabilizes the undesired eigenstates and relies on a probabilistic analysis to prove convergence. In contrast, we here associate the state observer to an adaptive version of so-called Markovian feedback (essentially, proportional control) and we show that this leads to a global exponential convergence property with a strict Lyapunov function. Furthermore, besides the instantaneous measurement output, our controller only depends on the single coordinate along the measurement axis, which opens the way to replacing the full state observer by lower-complexity filters in the future.
We propose a new method for pure-state and subspace preparation in quantum systems, which employs the output of a continuous measurement process and switching dissipative control to improve convergence speed, as well as robustness with respect to the initial conditions. In particular, we prove that the proposed closed-loop strategy makes the desired target globally asymptotically stable both in mean and almost surely, and we show it compares favorably against a time-based and a state-based switching control law, with significant improvements in the case of faulty initialization.