In a quantum computer the processing (thinking) takes place either in computers in Everett's many worlds or else in the many dimensional Hilbert space. (Depending upon your interpretation of quantum mechanics.) If our brains were quantum computers then there just might be a world of mind which is distinct from the physical world that our bodies occupy. (The ordinary 4 space.) This is much like the spirit-body dualism of Descartes and others.
My own view is that thought and mind are classical phenomena like those described on my website: www.robert-w-jones.com, philosopher, theory of thought and mind.
It might be interesting to run something like my AI Asa H on a quantum computer, of course. Might this produce a hypermind in its own universe?