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's an overview of the "quantum mind" debate among academics (whether quantum effects play an important role in the function of the brain) in FHI's Whole Brain Emulation Roadmap (page 37). This isn't quite the same question you're asking (since even if the brain uses quantum computing, an AI may be able to avoid it through some kind of algorithmic workaround), but I'd guess that most supporters of the "quantum mind" hypotheses would also answer "yes" to your question.
Really? I think it's plausible that quantum effects play an important role in the brain, but I'd be very surprised if that was actually an obstacle to AI.