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paulfchristiano comments on [Link] New paper: "The quantum state cannot be interpreted statistically" - Less Wrong Discussion
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No interpretation of quantum mechanics says anything at all about the extent of BQP, which is (as you well know) a purely mathematical question that has nothing to do with the laws of physics.
MWI implies that quantum computers compute BQP, and depending on how you specify Copenhagen, it implies either that quantum computers compute P or that they compute some mystical complexity class whose definition depends on the notion of "observer." This is the sense in which quantum computation provides evidence for MWI. Your comment is unrelated to the reasons for Scott Aaronson's agnosticism.
I think we're discussing different aspects. The essential argument for MWI based on computational issues I'm addressing is that in the second to last paragraph of the above post:
The problem with that sort of argument is that it proves too much since one would then have to explain why one in fact only gets a bit more computational power over classical systems.
I don't see what you mean. Quantum computers seem to use this additional resource which is not available classically, as the existence of any classically impossible quantum algorithm shows. This argument doesn't show that quantum computers get arbitrary access to this additional resource.
If I claim to have access to non-classical physics and show you one classically impossible feat, you should probably accept my argument. It is not compelling if you say "but what about this other classically impossible feat which you cannot achieve" and then ignore the explanation.
Well, but no one is disagreeing that quantum computers have access to non-classical resources. The problem is that explaining that by saying one has access to resources in other parts of the wavefunction creates the question "why do you only have a tiny bit of access" which about as large a question. It isn't at all clear that that's at all more satisfactory than simply saying that the actual laws of physics don't work as our intuition would expect them to.
Because the effect of the waveform drops off quickly with distance.
MWI predicts that it should be difficult to use these resources. Classical physics predicts that it should be impossible. Ergo, the fact that they're difficult to access is evidence for MWI.
Exactly. It makes no difference how powerful quantum computers are for Deutsch's argument. If we had waited exponential time for a classical computer to do it, we would not wonder "where the number was factored." Waiting only polynomial time for it to be factored then begs the question.
I am well aware of the extremely interesting complexity limitations of quantum computing. It definitely only extends computational capability a little bit -- and we still can't even prove that P does not equal NP. But none of this is relevant to Deutsch's "where was the number factored" argument. He is saying that if quantum states are physically real and not just a calculational tool, then you have to give a physical account of how Shor's algorithm works and the orthodox views of wavefunction collapse could not do that.