While writing my article "Could Robots Take All Our Jobs?: A Philosophical Perspective" I came across a lot of people who claim (roughly) that human intelligence isn't Turing computable. At one point this led me to tweet something to the effect of, "where are the sophisticated AI critics who claim the problem of AI is NP-complete?" But that was just me being whimsical; I was mostly not-serious.
A couple times, though, I've heard people suggest something to the effect that maybe we will need quantum computing to do human-level AI, though so far I've never heard this from an academic, only interested amateurs (though ones with some real computing knowledge). Who else here has encountered this? Does anyone know of any academics who adopt this point of view? Answers to the latter question especially could be valuable for doing article version 2.0.
Edit: This very brief query may have given the impression that I'm more sympathetic to the "AI requires QC" idea than I actually am; see my response to gwern below.
As a pedantic note, if you want to derandomize algorithms it is necessary (and sufficient) to assume P/poly != E, i.e. polynomial size circuits cannot compute all functions computed by exponential time computations. This is much weaker than P != NP, and is consistent with e.g. P = PSPACE. You don't have to be able to fool an adversary, to fool yourself.
This is sometimes sloganized as "randomness never helps unless non-uniformity always helps," since it is obvious that P << E and generally believed that P/poly is about as strong as P for "uniform" problems. It would be a big shock if P/Poly was so much bigger than P.
But of course, in the worlds where you can't derandomize algorithms in the complexity-theoretic sense, you can still look up at the sky and use the whole universe to get your randomness. What this means is that you can exploit much of the stuff going on in the universe to do useful computation without lifting a finger, and since the universe is so much astronomically larger than the problems we care about, this is normally good enough. General derandomization is extremely interesting and important as a conceptual framework in complexity theory, but useless for actually computing things.
Are you referring to this result? Doesn't seem to be identical to what you said, but very close.