But if you do think of it that way, why not just pick a random number using some quantum process, classically test whether or not it's a divisor of the number you're trying to factor, and kill yourself if it's not? In every universe where you survive (which, for sake of argument, are the only ones you care about) you find a factor on the first try.
I think you may have accidentally discovered the Quantum Bag Holder Paradox.
The algorithm generates a random permutation of its input using a quantum source of entropy, checks if the list is sorted, and, if it is not, destroys the universe. Assuming that the many-worlds interpretation holds, the use of this algorithm will result in at least one surviving universe where the input was successfully sorted in O(n) time.
In every universe where you survive (which, for sake of argument, are the only ones you care about) you find a factor on the first try.
You have to think that the odds really aren’t in your favor there.
(What, did you think this logic is only valid when you're trying to gain godlike powers?)
Postselection is ridiculously powerful, as you've noted.
That's the nature of true randomness, if you set up a dice throw a million times they could just as well all come up as six. Incredibly unlikely, but possible.
Also quantum parallel universe is not what you expect parallel universe to be. Universes interact with each other.
the entire planet is obliterated except in cases pursuant to their interests, with none the wiser since in those cases, they 'didn't do anything'
All universes affect the probability of something occurring in each universe. That is how each universe contributes a bit of the Fourier offset which gives off the period in pretty much all universes.
Because finding the right divisor is so unlikely, you run a high risk of killing yourself in all universes. As Scott emphasizes, quantum computers don’t run possibilities in parallel!