In this paper, we consider the quantum magnetohydrodynamic model for quantum plasmas. We first derive uniform estimates for the global smooth solutions in terms of the quantum coefficient \(\hbar \) and the Hall coefficient \(\epsilon \) . Then we establish the existence of global solutions and derive optimal convergence rates using the energy method. Next, applying the Lions-Aubin lemma, we prove that the unique smooth solution of the three-dimensional Hall-quantum-magnetohydrodynamic system converges globally in time to the smooth solution of the three-dimensional Navier-Stokes system as \(\hbar \) and \(\epsilon \) tend to zero. Furthermore, we provide the convergence rate estimates for any given positive time.
