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.
No serious neurologists actually consider quantum effects inside microtubules or arrangements of phosporyulation on microtubules or whatever important for neuron function. They're all either physicists who don't understand the biology or computer scientists who don't understand the biology. Nothing happens in neural activity or long-term-potentiation or other processes that cannot be accounted for by chemical processes, even if we don't understand exactly the how of some of them. The open questions are mostly exactly how neurons are able to change their excitability and structure over time and how they manage to communicate in large scale systems.
Actually, protein phosphorylation (like many other biochemical and biophysical processes, such as ion channel gating) is based on quantum tunneling. It may well be irrelevant, as the timing of the process can probably be simulated well enough with pseudo-random numbers, but on an off-chance that "true randomness" is required, a purely classical approach might be inadequate.