Quantum brains? Orchestrated objective reduction is a highly controversial theory that (amongst other things) posits quantum computation in the brain as a basis for human consciousness. The originators of the theory (Sir Roger Penrose and Stuart Hameroff) are now claiming that some recent discoveries provide evidentiary support for their theory.
I don't know enough about either their theories or the recent discoveries to make any judgment about the truth of the claims, or their strength. Until some widely accepted evidence appears, I will continue to look at this with skepticism.
There is one part of this theory that I find most satisfying: it's the only theory of consciousness that explains our brain's astounding feats of pattern recognition – feats that are unmatched by any supercomputer. We exercise these feats every day without thought, as they are effortless for us. Reading and comprehending a book is perhaps the canonical example – no computer has ever even come close to doing that, and the biggest reason is that computers are terrible at pattern recognition (but humans are great at it). Another example: human ability to comprehend speech in a room filled with people speaking. Another: human observational skills – we can easily pick the particular elements we're interested in out of our visual field – while we're moving, our eyes are moving, and our target is moving. Computers still can't even come close to that ability. True quantum computing occurring in our brains would provide a plausible mechanism for our pattern-matching abilities...
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