The "tricky bit" is not in branching out, it's in collapsing back down to determinism again. When you do your measurement at the end of the process, if you hav

The "tricky bit" is not in branching out, it's in collapsing back down to determinism again. When you do your measurement at the end of the process, if you have a mixed state you'll just pick one of the "parallel computations" -- you can't just "pick the best one". Put simply, it's like a nondeterministic Turing machine that branches randomly instead of taking "all paths at once." Where quantum computers are meant to get their extra power is in what's called "destructive interference". The idea here is that there aren't really classical probabilities associated with the computation branches, there are complex "amplitude" numbers that square to give probabilities. When your computation is laid out in the right way, you want the amplitudes of the "bad" paths in the computation to cancel out, so when you take a measurement at the end all you're left choosing between are "good" paths.