There has to be some misinterpretation going on here (or David Deutsch just hasn't thought this through). You can have a quantum computer in a superposition of states, but that isn't many worlds; to have many worlds, the computer has to interact with the outside world and split the outside world into a corresponding superposition of states. Such interaction with the outside world prevents a quantum computer from functioning - and it's precisely such information leakage to the outside world that is a major difficulty when trying to scale up quantum computers.