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We have carried out path-integral molecular dynamics simulations for hydrated sulfuric acid clusters to understand acid-dissociation and hydrogen-bonded structural rearrangement processes in these clusters from a quantum mechanical viewpoint. The simulations were performed using the PM6 semiempirical electronic structure level whose parameters were modified on the basis of the specific reaction parameters strategy so that relative energies of optimized structures, as well as water binding energies reproduce ab initio and density-functional theory calculations. We have found that the acid dissociation processes, first and second deprotonation, effectively occur in a hydrated cluster with a specific cluster size. The mechanisms of the proton-transfer processes were analyzed in detail and it was found that the distance between O in sulfuric acid and O in the proton-accepting water is playing an important role. We also found that the water coordination number of the poton-accepting water is important in the proton-transfer processes.