The statement about performing logic on all that data in parallel is misleading, at best.
That does mean that the result you get from the calculation can be nothing more than the classical equivalent, but the amount of inputs to that result, and the resultant enormous explosion of processing you can do on it (each operation yielding potentially exponential growth in evaluated possibilities), is dependent on other factors.
I was thinking of http://en.wikipedia.org/wiki/Hidden_variable_theory and that those could be properties of particles skewed into extra dimensions.
This is way over my math and physics skill, but it's still very fascinating.
Anyway, that's not quite true, you can get there by giving up principle of locality or counterfactual definiteness. And in theory nothing requires the principle of locality to be true.