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

arXiv:2602.12472 · IEEE International Conference on Quantum Control, Computing and Learning (qCCL)

Dynamic Programming Principle and Stabilization for Mean-Field Quantum Filtering Systems

Sofiane Chalal, Nina H. Amini, Hamed Amini, Mathieu Laurière

quant-phmath.OCSubmitted Feb 12, 2026• Announced Feb 16, 2026• 0 citations
arXivHTMLPDF

Abstract

Working within the quantum filtering framework, we establish a dynamic programming principle in an infinite-dimensional setting by embedding the state space into the Hilbert-Schmidt space. We then study a stabilization problem for continuously monitored Ising-coupled qubits and, in the mean-field limit, demonstrate quantum state reduction together with exponential convergence toward prescribed eigenstates under suitable feedback laws.

Related papers

Quantum filtering and propagation of chaos for open quantum systems, with applications to quantum feedback control and quantum mean-field games

Vassili Nikitich Kolokoltsov

The theory of quantum filtering (of quantum continuous measurements) was developed by V.P. Belavkin about 40 years ago. Since then it attracted attention of numerous investigators including mathematicians, theoretical and experimental physicists. However, the rigorous mathematical theory of the filtering equations for mixed states in basic infinite-dimensional quantum systems remained an open problem, which was resolved by the author recently. This survey paper presents in full the mathematical theory of quantum filtering equations, their rigorous derivation from basic principles, the corresponding law of large number limits (propagation of chaos) and related topics. Applications to feedback control, quantum dynamic and mean-field games are discussed.

arXiv:2607.08507•Jul 9, 2026•0 citations

Tractable Infinite-Horizon Stochastic Model Predictive Control for Quantum Filtering via Eigenstate Reduction

Yunyan Lee, Ian R. Petersen, Daoyi Dong

Model predictive control has shown potential to enhance the robustness of quantum control systems. In this work, we propose a tractable Stochastic Model Predictive Control (SMPC) framework for finite-dimensional quantum systems under continuous-time measurement and quantum filtering. Using the almost-sure eigenstate reduction of quantum trajectories, we prove that the infinite-horizon stochastic objective collapses to a fidelity term that is computable in closed form from the one-step averaged state. Consequently, the online SMPC step requires only deterministic propagation of the filter and a terminal fidelity evaluation. An advantage of this method is that it eliminates per-horizon Monte Carlo scenario sampling and significantly reduces computational load while retaining the essential stochastic dynamics. We establish equivalence and mean-square stability guarantees, and validate the approach on multi-level and Ising-type systems, demonstrating favorable scalability compared to sampling-based SMPC.

quant-pharXiv:2511.05916•Nov 11, 2025•0 citations

Quantum Feedback Cooling Without State Filtering

Lorenzo Franceschetti, Francesco Ticozzi

We introduce a dynamic state-based feedback law that stabilizes quantum states or subspaces associated with extremal values of a continuously monitored observable - a problem motivated by quantum cooling tasks. We then propose an output-based approximation that uses simple filtering of the measurement record to emulate the required feedback signal, thereby avoiding full real-time quantum state estimation, a key bottleneck for implementing and scaling filtering-based feedback control. The performance of the resulting strategy is demonstrated numerically on two test-bed models for feedback cooling.

IEEE Control Systems Letters•Jan 1, 2026•0 citations

Quantum Feedback Cooling without State Filtering

Lorenzo Franceschetti, Francesco Ticozzi

We introduce a state-based feedback law that stabilizes quantum states or subspaces associated with extremal values of a continuously monitored observable - a problem motivated by quantum cooling tasks. We then propose an output-based approximation that uses simple filtering of the measurement record to emulate the required feedback signal, thereby avoiding full real-time quantum state estimation, a key bottleneck for implementing and scaling filtering-based feedback control. The performance of the resulting strategy is demonstrated numerically on two test-bed models for feedback cooling.

quant-pharXiv:2603.06370•Mar 9, 2026•0 citations

Stabilization of Time-Varying Perturbed Quantum Systems via Reduced Filters

Weichao Liang, Daoyi Dong

In practical applications, quantum systems are inevitably subject to significant uncertainties, including unknown initial states, imprecise physical parameters, and unmodeled environmental noise, all of which pose major challenges to robust quantum feedback control. This paper proposes a feedback stabilization strategy based on a reduced quantum filter that achieves robustness against time-varying Hamiltonian perturbations and additional dissipative effects, without requiring prior knowledge of the initial state or exact system parameters. The proposed filter estimates only O(N) real variables corresponding to the diagonal elements of the system density matrix in a quantum non-demolition basis in contrast to the O(N^2) variables required by a full stochastic master equation, where N is the Hilbert space dimension. This dimensionality reduction substantially simplifies real-time computation and feedback implementation while preserving both convergence and robustness guarantees. Rigorous analysis further establishes global exponential stability of the target subspace. The results provide a scalable framework for robust and efficient measurement-based feedback control applicable to high-dimensional perturbed open quantum systems.

math-phCross-listedarXiv:2511.07949•Nov 12, 2025•0 citations

Measurement-Based Feedback of Open Quantum Systems: A Control-Theoretic Review and Tutorial

Weichao Liang, Jing Zhang, Gaoyue Guo +1 more

This review develops a control-theoretic perspective on measurement-based feedback for continuously monitored open quantum systems, with the main analysis focused on finite-dimensional systems governed by diffusive stochastic master equations. We introduce the relevant state-space, invariant-subspace, and quantum non-demolition structures, interpret quantum filtering as nonlinear observer dynamics, and review open-loop asymptotics, filter stability, state-feedback stabilization, robustness, and reduced-order observer-based control. Particular emphasis is placed on a recurrence--contraction framework, in which Hamiltonian feedback removes non-target invariant obstructions while measurement-induced dynamics provide local exponential contraction. Although the detailed analysis is developed for finite-dimensional diffusive models, the underlying measurement--estimation--feedback architecture is relevant across a broad range of quantum platforms. We further discuss implementation challenges and open problems involving scalable estimation, sampling and delay, adaptation, hybrid and non-Markovian dynamics, practical stability, optimal control, and learning-based design. By organizing these developments around invariance, estimation, recurrence, and contraction, the review provides a tutorial bridge between measurement-based quantum feedback and nonlinear stochastic control.

quant-pharXiv:2609.06111•Sep 8, 2026•0 citations
Working within the quantum filtering framework, we establish a dynamic programming principle in an infinite-dimensional setting by embedding the state space into the Hilbert-Schmidt space. We then study a stabilization problem for continuously monitored Ising-coupled qubits and, in the mean-field limit, demonstrate quantum state reduction together with exponential convergence toward prescribed eigenstates under suitable feedback laws.
The theory of quantum filtering (of quantum continuous measurements) was developed by V.P. Belavkin about 40 years ago. Since then it attracted attention of numerous investigators including mathematicians, theoretical and experimental physicists. However, the rigorous mathematical theory of the filtering equations for mixed states in basic infinite-dimensional quantum systems remained an open problem, which was resolved by the author recently. This survey paper presents in full the mathematical theory of quantum filtering equations, their rigorous derivation from basic principles, the corresponding law of large number limits (propagation of chaos) and related topics. Applications to feedback control, quantum dynamic and mean-field games are discussed.
Model predictive control has shown potential to enhance the robustness of quantum control systems. In this work, we propose a tractable Stochastic Model Predictive Control (SMPC) framework for finite-dimensional quantum systems under continuous-time measurement and quantum filtering. Using the almost-sure eigenstate reduction of quantum trajectories, we prove that the infinite-horizon stochastic objective collapses to a fidelity term that is computable in closed form from the one-step averaged state. Consequently, the online SMPC step requires only deterministic propagation of the filter and a terminal fidelity evaluation. An advantage of this method is that it eliminates per-horizon Monte Carlo scenario sampling and significantly reduces computational load while retaining the essential stochastic dynamics. We establish equivalence and mean-square stability guarantees, and validate the approach on multi-level and Ising-type systems, demonstrating favorable scalability compared to sampling-based SMPC.
We introduce a dynamic state-based feedback law that stabilizes quantum states or subspaces associated with extremal values of a continuously monitored observable - a problem motivated by quantum cooling tasks. We then propose an output-based approximation that uses simple filtering of the measurement record to emulate the required feedback signal, thereby avoiding full real-time quantum state estimation, a key bottleneck for implementing and scaling filtering-based feedback control. The performance of the resulting strategy is demonstrated numerically on two test-bed models for feedback cooling.
We introduce a state-based feedback law that stabilizes quantum states or subspaces associated with extremal values of a continuously monitored observable - a problem motivated by quantum cooling tasks. We then propose an output-based approximation that uses simple filtering of the measurement record to emulate the required feedback signal, thereby avoiding full real-time quantum state estimation, a key bottleneck for implementing and scaling filtering-based feedback control. The performance of the resulting strategy is demonstrated numerically on two test-bed models for feedback cooling.
In practical applications, quantum systems are inevitably subject to significant uncertainties, including unknown initial states, imprecise physical parameters, and unmodeled environmental noise, all of which pose major challenges to robust quantum feedback control. This paper proposes a feedback stabilization strategy based on a reduced quantum filter that achieves robustness against time-varying Hamiltonian perturbations and additional dissipative effects, without requiring prior knowledge of the initial state or exact system parameters. The proposed filter estimates only O(N) real variables corresponding to the diagonal elements of the system density matrix in a quantum non-demolition basis in contrast to the O(N^2) variables required by a full stochastic master equation, where N is the Hilbert space dimension. This dimensionality reduction substantially simplifies real-time computation and feedback implementation while preserving both convergence and robustness guarantees. Rigorous analysis further establishes global exponential stability of the target subspace. The results provide a scalable framework for robust and efficient measurement-based feedback control applicable to high-dimensional perturbed open quantum systems.
This review develops a control-theoretic perspective on measurement-based feedback for continuously monitored open quantum systems, with the main analysis focused on finite-dimensional systems governed by diffusive stochastic master equations. We introduce the relevant state-space, invariant-subspace, and quantum non-demolition structures, interpret quantum filtering as nonlinear observer dynamics, and review open-loop asymptotics, filter stability, state-feedback stabilization, robustness, and reduced-order observer-based control. Particular emphasis is placed on a recurrence--contraction framework, in which Hamiltonian feedback removes non-target invariant obstructions while measurement-induced dynamics provide local exponential contraction. Although the detailed analysis is developed for finite-dimensional diffusive models, the underlying measurement--estimation--feedback architecture is relevant across a broad range of quantum platforms. We further discuss implementation challenges and open problems involving scalable estimation, sampling and delay, adaptation, hybrid and non-Markovian dynamics, practical stability, optimal control, and learning-based design. By organizing these developments around invariance, estimation, recurrence, and contraction, the review provides a tutorial bridge between measurement-based quantum feedback and nonlinear stochastic control.