Math or it didn't happen.
Speculation without hard facts to back it up is poppycock gobbledygook.
https://en.wikipedia.org/wiki/Quantum_mind
if true, appears to support his claim, assuming that if we do have quantum minds that they cannot be simulated by non-quantum computers. Roger Penrose is certainly well-respected. I don't have a strong opinion either way.
It's fun to think about "what if our thoughts are the universe itself!" but it's so blatantly wrong. It's just one step away from saying consciousness is "mystical" or created by philotic twining.
Everything will -- somehow -- be better. Just add quantum. (protip: go read scott aaronson's relevant articles, papers, monographs, course materials, etc).
I don't claim the effects aren't present. I do claim they are unnecessary for the emergence of human level consciousness and the reproduction thereof in silicon.
What bothers me about all of this is that he writes books about it aimed at the general population, instead of proposing his ideas properly. Inevitably many of the laymen who casually encounter his ideas will misunderstand his point entirely and mistakenly think that Penrose supports a non-materialistic view of the mind (which of course he does not. A mind as Penrose envisions it, despite not being algorithmic, is still quite materialistic).
Roger Penrose is a brilliant man, but I think this is a case of the Nobel Disease (well, he hasn't received a Nobel prize, but even so).
It's also possible that consciousness is better understood as a computational process which is implemented on a VM instantiated by a brain. In that case looking too hard at the squishy stuff is not directly relevant and may be distracting, since it's a very complex way to implement a computer. This is logically possible and is of historic significance in AI.
My view is that the everyday concept of consciousness is mistaken, and that no such thing will be found. Our common sense view of perception and cognition has been found over and over to be completely wrong, so we shouldn't expect consciousness to turn up anywhere just because it feels like it ought too.
Functional approaches to brain modelling neatly avoid this issue by just building away and not worrying about it.
TLDR: physical doesn't mean explicable, and consciousness won't be explained by a physical process since it doesn't exist.
What makes a quantum computer better at AI?
The thing is, even Penrose isn't proposing anything mystical being done by quantum mechanics. He doesn't like the idea of an algorithmic mind, so he invokes quantum phenomenon to make the mind technically no longer algorithmic. In the real world though, nothing prevents you from doing similar with a desktop computer. You an rig together a (crappy) RNG for your x86 desktop with a serial port and a smoke detector. Penrose isn't trying to suggest that intelligence could not be replicated in man made machines, but rather suggest that the human mind is not restricted as we know purely algorithmic systems to be.