I don't really understand what this means - you obviously know at the smallest level things happen by random probability - because you mention the quantum world - but then you say the universe is deterministic.
Bringing up 'Quantum' effects to somehow free us from determinism and somehow introduce free will, is completely false. Somehow using the word "Quantum" explains human consciousness is wrong.
A coin flip is still determined. You don't know which way it will flip, but also, you aren't deciding which way it will flip. The future is determined either way, determined one way, or determined the other way.
Not sure if any other wizard hat things than those can extend classical digital computing
We don't actually know this. It is just what we observe that fits our map so far.
neurons aren't binary. who knows if they're special in a way digital computers can't simulate -- they aren't well understood.
nobody said anything about determinism besides you
Most of the time someone brings up the word 'Digital' they are talking about 1's and 0's, and how everything is known and determined, and thus looses the ineffable human quality.
"they're special in a way digital computers can't simulate"
I might be making a straw man, but you are literally just saying "something magical that exists outside physics must be going on"
But it would be the case that the universe is non-computable, and if this is the case, even without "magic", you would not be able to reproduce certain kinds of things (even not conscious ones) with a computer.