2023/03/16 by Sofiane Chalal, Nina H. Amini, Chalal, Sofiane +3 · 1 citation
Computer Science · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC) #Probability (math.PR) #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum optics and atomic interactions
paper · doi:10.48550/arxiv.2303.09667
openalex publication_date 2023/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Following Kolokoltsov's work [1], we present an extension of mean-field control theory in quantum framework. In particular such an extension is done naturally by considering the Belavkin quantum filtering and control theory in a mean-field setting. In this setting, the dynamics is described by a controlled Belavkin equation of McKean-Vlasov type. We prove the well-posedness of such an equation under imperfect measurement records. Furthermore, we show under purification assumption the propagation of chaos for perfect measurements. Finally, we apply particle methods to simulate the mean-field Belavkin equation and we provide numerical simulations showing the stabilization of the mean-field Belavkin equation by a feedback control strategy towards a chosen target state.