If quantum computers would work, it would be very difficult to explain "where" the computation happens without having some sort of MWI into picture. But if, somehow, quantum computers keep their noise levels up without producing any interesting acceleration I'll expect that a theory would emerge at some point explaining that. And it may disambiguate which interpretation is the one.
Quantum computers are easy to explain in CI as well: they simply exploit certain numerical properties of complex-valued probabilities (unlike the real-valued probabilities of classical probabilistic Turing machines).
