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.
There are also intros available for free on Oded Goldreich's FoC website.
Here's my simplified intuitive explanation for people not interested in learning about these technical concepts. (Although of course they should!) Suppose you're playing rock-paper-scissors with someone and you're using a pseudorandom number generator, and P=NP, then your opponent could do the equivalent of trying all possible seeds to see which one would reproduce your pattern of play, and then use that to beat you every time.
In non-adversarial situations (which may be what Eliezer had in mind) you'd have to be pretty unlucky if your cognitive algorithm or environment happens to serve as a distinguisher for your pseudorandom generator, even if it's technically distinguishable.