Are you leaving the reason unsaid, or am I in fact reading your argument correctly: "We don't understand consciousness, and we don't understand quantum, therefore it is likely consciousness relies on quantum." There's already plenty of mystery in an ordinary deterministic computation-driven approach to intelligence.
> > we have no reason to believe intelligence relies on [as-yet mysterious aspects of quantum physics]
you wrote
> We actually do have reason to believe that ...
and later clarified
> [some true premises], therefore there may be unknown physics involved in consciousness, and those unknown physics may not be computable.
Saying something could be is different from saying we have reason to believe it. There may be a soul. Absent convincing evidence of the soul, though, we shouldn't predicate other research on the idea that it exists.