Two new quantum simulation methods, which we developed recently based on the Metropolis and self-consistent algorithms defined as QMC and SCA approaches respectively, were employed to investigate the magnetic properties of an antiferromagnetic nanoparticle with strong surface anisotropy. All simulations were started from a random magnetic configuration and carried out from a temperature well above the phase transition stepwise down to very low temperatures as other researchers have been doing in classical Monte Carlo (CMC) simulations. It turns out that the magnetic structures, magnetizations, total (free) energy, magnetic entropy and specific heat calculated by means of the two approaches are well consistent with each other, thereby verifying their correctness mutually.