Neuroscience isn't a subset of computer science. It's a study of biological nervous systems, which can involve computational models, but it's not limited to that. You're mistaking a kind of map (computation) for the territory, probably based on a philosophical assumption about reality.
At any rate, biological organisms are not like LLMs. The nervous systems of human may perform some LLM-like actions, but they are different kinds of things.
But computational models are possibly the most universal thing there is, they are beneath even mathematics, and physical matter is no exception. There is simply no stronger computational model than a Turing machine, period. Just because you make it out of neurons or silicon is irrelevant from this aspect.
Turing machines aren't quantum mechanical, and computation is based on logic. This discussion is philosophical, so I guess it's philosophy all the way down.
Turing machines are deterministic. Quantum Mechanics is not, unless you go with a deterministic interpretation, like Many Worlds. But even then, you won't be able to compute all the branches of the universal wave equation. My guess is any deterministic interpretation of QM will have a computational bullet to bite.
As such, it doesn't look like reality can be fully simulated by a Turing machine.
Giving a Turing machine access to a quantum RNG oracle is a trivial extension that doesn't meaningfully change anything. If quantum woo is necessary to make consciousness work (there is no empirical evidence for this, BTW), such can be built into computers.
At any rate, biological organisms are not like LLMs. The nervous systems of human may perform some LLM-like actions, but they are different kinds of things.