Scott Aaronson's blog notably states:
Quantum computers would not solve hard search problems instantaneously by simply trying all the possible solutions at once.
Is this a statement of a law, as in, is there some no-go theorem that prevents this, or is this a statement about what we know, that is, it's possible in theory, but we have not found an algorithm that does this?
Edit: People are pointing out that the word 'simply' carries the meaning of the popular science explanations, whereby once the quantum state contains all the possible amplitudes, then the computer tells us the one we're looking for.
Now, the first part seems manifestly possible to me. It's not hard to create a quantum state who's amplitudes do represent all the possibilities at once. So what if we drop the word 'simply' from his statement. Is there some complicated mechanism that can cancel out all the other possibilities?
It seems like as long as 1) Every gate is unitary and 2) Every measurement is Hermitian, it's a valid quantum circuit. And the task is to determine that to-be-specified complicated mechanism.
Why isn't this an active area of research?