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.
Quantum computers can be simulated on classical computers with exponential slow down. So even if you think the human mind uses quantum computation, this doesn't mean that the same thing can't be done on a classical machine. Note also that BQP (the set of efficiently computable problems by a quantum computer) is believed (although not proven) to not contain any NP complete problems.
Note also that at a purely practical level, since quantum computers can do a lot of things better than classical computers and our certainty about their strength is much lower, trying to run an AI on a quantum computer is a really bad idea if you take the threat of AI going FOOM seriously.
An exponential slowdown basically means that it can't be done. If you have an oracle for EXPTIME then you're basically already set for most problems you could want to solve.