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.
So that is practically true, and in fact. EXPTIME is one of the few things we can show is large enough that we can even prove it properly contains P. But, in context this isn't as bad as it looks. The vast majority of interesting things we can do on quantum computers take in practice much less than exponential time (look at factoring for example). In fact, BQP actually lives inside PSPACE, so this shouldn't be that surprising.
But practical issues aside , most of the arguments about using quantum computers to do AI or consciousness involve claims that they are fundamentally necessary. The fact that we can simulate them with sufficient slow down demonstrates that at least that version of that thesis is false.