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Proceedings of the ... American Control Conference/Proceedings of the American Control Conference

Sliding mode control of two-level quantum systems with bounded uncertainties

Daoyi Dong, Ian R. Petersen

Published Jun 1, 2010• 7 citations
Publisher

Abstract

This paper proposes a robust control method based on sliding mode design for two-level quantum systems with bounded uncertainties. An eigenstate of the two-level quantum system is identified as a sliding mode. The objective is to design a control law to steer the system into the sliding mode domain and then maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. For different uncertainties, we give conditions for designing a control law, which can guarantee the desired robustness in the presence of the uncertainties. The sliding mode control method has potential applications to quantum information processing with uncertainties.

DOI
10.1109/acc.2010.5530580

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This paper proposes a robust control method based on sliding mode design for two-level quantum systems with bounded uncertainties. An eigenstate of the two-level quantum system is identified as a sliding mode. The objective is to design a control law to steer the system into the sliding mode domain and then maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. For different uncertainties, we give conditions for designing a control law, which can guarantee the desired robustness in the presence of the uncertainties. The sliding mode control method has potential applications to quantum information processing with uncertainties.
This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). SMC is a widely used approach in classical control theory and industrial applications. We show that SMC is also a useful method for robust control of quantum systems. In this paper, we define two specific classes of sliding modes (i.e. eigenstates and state subspaces) and propose two novel methods combining unitary control and periodic projective measurements for the design of quantum SMC systems. Two examples including a two-level system and a three-level system are presented to demonstrate the proposed SMC method. One of the main features of the proposed method is that the designed control laws can guarantee the desired control performance in the presence of uncertainties in the system Hamiltonian. This SMC approach provides a useful control theoretic tool for robust quantum information processing with uncertainties.
This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). SMC is a widely used approach in classical control theory and industrial applications. We show that SMC is also a useful method for robust control of quantum systems. In this paper, we define two specific classes of sliding modes (i.e. eigenstates and state subspaces) and propose two novel methods combining unitary control and periodic projective measurements for the design of quantum SMC systems. Two examples including a two-level system and a three-level system are presented to demonstrate the proposed SMC method. One of the main features of the proposed method is that the designed control laws can guarantee the desired control performance in the presence of uncertainties in the system Hamiltonian. This SMC approach provides a useful control theoretic tool for robust quantum information processing with uncertainties.
This paper presents a sampled-data control approach based on sliding mode design for the robust control of a two-level quantum system, where the control law can be designed offline and then be used online for a quantum system with bounded uncertainties in the system Hamiltonian. Such a control law consists of a periodic sampling process and a Lyapunov control design. A sufficient condition on the relationships between related parameters in the control system is established and the Lyapunov control design is demonstrated by simulation, which can be used to show the required robustness of the quantum system in the presence of uncertainties.
Robustness is a major issue in the stabilization control of quantum systems. A practical quantum system is often exposed to uncertainties and disturbances in external fields and system Hamiltonian. Sliding mode control is a powerful tool in designing robust control for classical systems to mitigate the effect of disturbances. This paper leverages the sliding mode control technique to design a finite-time reaching law for two-level quantum systems in the presence of uncertainties in the system Hamiltonian. A numerical example is presented to showcase the effectiveness of the theoretical results. This research contributes to advancing the robust control techniques for quantum systems, paving the way for enhanced stability in quantum computing and quantum information processing applications.
Due to the influence of decoherence, the quantum state probably evolves from the initial pure state to the mixed state, resulting in loss of fidelity, coherence and purity, which is deteriorating for quantum information transmission. Thus, in quantum engineering, quantum control should not only realize the transfer and track of quantum states through manipulation of the external electromagnetic field but also enhance the robustness against decoherence. In this paper, we aim to design a control law to steer the system into the sliding mode domain and maintain it in that domain when bounded uncertainties exist in the system Hamiltonian. We first define the required control performance by fidelity, degree of coherence and purity in terms of the uncertainty of the Hamiltonian in Markovian open quantum system. By characterizing the required robustness using a sliding mode domain, a sampled-data design method is introduced for decoherence control in the quantum system. Furthermore, utilizing the sampled data, a control scheme has been designed on the basis of sliding mode control, and the choice of sampling operator and driving of quantum state during the sampling by the Lyapunov control method are discussed.
In this paper, a new quantum sliding mode control, for improving the performance of the two-level quantum sliding mode control systems with bounded uncertainties, is introduced. The presented quantum sliding surface is based on the error which occurs between the predetermined sliding mode and the system state. The control objective is to derive the system state to reach the sliding mode domain and then maintain its motion on it. For this purpose, we use the sliding mode control method and periodic projective measurements. A theorem for facilitating the presented method is proved. The simulated example shows that both the reaching time to the sliding mode and the control amplitude are significantly decreased, which demonstrate the effectiveness and validity of the presented method.