It's definitely a leap, but there's a decent amount of information (not proof however) on the subject laying around. We still don't understand how the brain brings about consciousness. I guess I should say it's not a huge leap to assume it has something to do with other things we also don't understand. Given quantum effect and number theory still elude us in areas, it's a decent approach to assume they might be related.
I've debugged problems in my code that, at first glance, appear to be unrelated to each other. Given something is slightly off in one area isn't a proof something of in another area is related, but it's a good place to start looking.
As far as I know there is a decent amount of information against the fact that brains are quantum computers.
On the other hand there is a talk by Hinton on youtube [1] that sheds interesting light on some variants of deep learning and the way the brain uses (classical) noise.
To the best of our knowledge it is still a pretty large leap of logic.