It does not. Quantum effects are a smokescreen for clinging onto the idea that "only humans can be human". BQP is quite easily contained in PSPACE, and more generally adding quantum operations does not move one beyond Turing machines (realistically - only something like a halting problem oracle does).
I think you missed the point of my comment. BQP (i.e. "stuff that is efficiently solvable by a quantum computer") is almost certainly bigger than P (i.e. "stuff that is efficiently solvable by classical computers"). There was not even remotely anything in my argument that was claiming "only humans can be human" or "only humans can be intelligent" or anything like that (that would have been a silly claim). And nothing remotely related to claiming quantum effects have anything to do with human brains.