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Communications and control engineering/Communications and control engineering series

Sliding Mode Control of Quantum Systems

Daoyi Dong, Ian R. Petersen

Published Jan 1, 2023• 7 citations
Publisher

Abstract

Sliding mode control is a powerful variable structure control method for classical control systems. The basic idea of sliding mode control can also be extended to the quantum domain for robust control. This chapter presents sliding mode control results for quantum systems. In Sect. 6.1, the concept of sliding mode control is introduced to the quantum domain and sliding modes are defined for quantum systems. Section 6.2 presents results on sliding mode control for two-level quantum systems. $$^\text {a}$$ Sliding mode control methods are extended to multi-level quantum systems in Sect. 6.3 $$^\text {b}$$ and then to open quantum systems in Sect. 6.4. $$^\text {c}$$ A summary and further reading are given in Sect. 6.5.

DOI
10.1007/978-3-031-20245-2_6

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Sliding mode control is a powerful variable structure control method for classical control systems. The basic idea of sliding mode control can also be extended to the quantum domain for robust control. This chapter presents sliding mode control results for quantum systems. In Sect. 6.1, the concept of sliding mode control is introduced to the quantum domain and sliding modes are defined for quantum systems. Section 6.2 presents results on sliding mode control for two-level quantum systems. a^\text {a}a Sliding mode control methods are extended to multi-level quantum systems in Sect. 6.3 b^\text {b}b and then to open quantum systems in Sect. 6.4. c^\text {c}c A summary and further reading are given in Sect. 6.5.
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.
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.
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.
State estimation and control of quantum systems present significant challenges due to the inherent noise, uncertainty, and non-linearity of quantum dynamics. In this paper, we propose the application of Sliding Mode Observers (SMOs) as a robust and efficient solution for the state estimation and control of finite dimensional quantum systems whose state is described by a density matrixρ\rhoρ. We demonstrate how these observers can be used to track quantum states accurately, despite the presence of measurement noise and system dynamics uncertainties. Furthermore, we introduce a control strategy that leverages the state estimates to stabilize the quantum system, ensuring desirable performance even under challenging conditions. Numerical simulations are provided to illustrate the effectiveness of the proposed methodology, showcasing improvements in system stability, accuracy of state estimation, and robustness to perturbations. The results highlight the potential of sliding mode observers as a viable tool for quantum control applications, including quantum information processing, quantum computing, and other emerging quantum technologies.