Alternating two fair coin flipping games can create a winning game. Such a Parrondo game is a discrete model for a thermal ratchet. Recently we have constructed quantum versions of these coin flipping games that display the same 'paradoxical' behavior. In this paper we add noise to these quantum Parrondo games in order that they can be compared with continuum models of quantum ratchets. Simulation of these models reproduces one of the most interesting features of quantum ratchets: current inversion.