Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Conference on Control Technology and Applications (CCTA)

Application of Sliding Mode Control & Observer to Stabilized Two-Level Quantum Systems

Kaydian Quintero, Bereket Berhane, Sergey V. Drakunov

Published Aug 25, 2025• 0 citations
Publisher

Abstract

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 matrix$\rho$. 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.

DOI
10.1109/ccta53793.2025.11151431

Related papers

Finite-Time Reaching Law Based Sliding Mode Control of Quantum Systems

Eram Taslima, Shyam Kamal, Ram Khelawan Saket

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.

International Workshop on Variable Structure Systems•Oct 21, 2024•5 citations

Sliding mode control of quantum systems

Daoyi Dong, Ian R. Petersen

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.

•Jan 1, 2009•91 citations

Sliding mode control of quantum systems

Daoyi Dong, Ian R Petersen

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.

arXiv:0911.0062•New Journal of Physics•Oct 30, 2009•104 citations

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

Daoyi Dong, Ian R. Petersen

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.

Proceedings of the ... American Control Conference/Proceedings of the American Control Conference•Jun 1, 2010•7 citations

Lyapunov-based stability analysis of quantum sliding mode controller

Youcef Malek, Nadjet Zioui, Mohamed Tadjine

This article addresses the lack of formal stability analyses in quantum sliding mode control (QSMC) by providing rigorous proof of stability and convergence based on Lyapunov theory. It also proposes an optimized QSMC approach that reduces quantum resource requirements while preserving control performance. The study begins with a re-evaluation of the conventional QSMC formulation, which implements the sign function using three qubits, along with a Hadamard gate and a CCNOT gate. A Lyapunov-based analysis is conducted to formally demonstrate the stability and convergence of the system. Based on this result, an improved QSMC scheme is introduced. The new design replaces the original structure with a quantum sign detector, a measurement process, and a rotation gate, thus reducing the implementation to two qubits. The proposed method is validated by its application to the speed control of a DC motor. The results show that it maintains efficient performance while requiring fewer computing resources. Simulation results support the feasibility of the approach. This work strengthens the theoretical foundations of QSMC and improves its applicability. The optimized version offers a more efficient and scalable solution for implementation on current quantum hardware with limited qubit availability.

International Journal of Innovative Research and Scientific Studies•May 4, 2026•0 citations

No-Collapse Accurate Quantum Feedback Control via Conditional State Tomography

Sangkha Borah, Bijita Sarma

The effectiveness of measurement-based feedback control protocols is hampered by the presence of measurement noise, which affects the ability to accurately infer the underlying dynamics of a quantum system from noisy continuous measurement records to determine an accurate control strategy. To circumvent such limitations, this Letter explores a real-time stochastic state estimation approach that enables noise-free monitoring of the conditional dynamics including the full density matrix of the quantum system using noisy measurement records within a single quantum trajectory-a method we name as "conditional state tomography." This, in turn, enables the development of precise measurement-based feedback control strategies that lead to effective control of quantum systems by essentially mitigating the constraints imposed by measurement noise and has potential applications in various feedback quantum control scenarios. This approach is particularly useful for reinforcement-learning-(RL) based control, where the RL-agent can be trained with arbitrary conditional averages of observables, and/or the full density matrix as input (observation), to quickly and accurately learn control strategies.

arXiv:2301.07254•Physical Review Letters•Nov 21, 2023•2 citations
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.
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.
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 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 article addresses the lack of formal stability analyses in quantum sliding mode control (QSMC) by providing rigorous proof of stability and convergence based on Lyapunov theory. It also proposes an optimized QSMC approach that reduces quantum resource requirements while preserving control performance. The study begins with a re-evaluation of the conventional QSMC formulation, which implements the sign function using three qubits, along with a Hadamard gate and a CCNOT gate. A Lyapunov-based analysis is conducted to formally demonstrate the stability and convergence of the system. Based on this result, an improved QSMC scheme is introduced. The new design replaces the original structure with a quantum sign detector, a measurement process, and a rotation gate, thus reducing the implementation to two qubits. The proposed method is validated by its application to the speed control of a DC motor. The results show that it maintains efficient performance while requiring fewer computing resources. Simulation results support the feasibility of the approach. This work strengthens the theoretical foundations of QSMC and improves its applicability. The optimized version offers a more efficient and scalable solution for implementation on current quantum hardware with limited qubit availability.
The effectiveness of measurement-based feedback control protocols is hampered by the presence of measurement noise, which affects the ability to accurately infer the underlying dynamics of a quantum system from noisy continuous measurement records to determine an accurate control strategy. To circumvent such limitations, this Letter explores a real-time stochastic state estimation approach that enables noise-free monitoring of the conditional dynamics including the full density matrix of the quantum system using noisy measurement records within a single quantum trajectory-a method we name as "conditional state tomography." This, in turn, enables the development of precise measurement-based feedback control strategies that lead to effective control of quantum systems by essentially mitigating the constraints imposed by measurement noise and has potential applications in various feedback quantum control scenarios. This approach is particularly useful for reinforcement-learning-(RL) based control, where the RL-agent can be trained with arbitrary conditional averages of observables, and/or the full density matrix as input (observation), to quickly and accurately learn control strategies.