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.
As such, it doesn't look like reality can be fully simulated by a Turing machine.