  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.
