If you agree that the universe is governed by the laws of quantum mechanics, that these laws are local, and that any given region of the universe can be describ

If you agree that the universe is governed by the laws of quantum mechanics, that these laws are local, and that any given region of the universe can be described with a finite dimensional Hilbert space (informally speaking, it contains a finite amount of information, which is implied by the Bekenstein bound), then yes. And of course there are some theories where these assumptions don't hold where the answer is still yes. See this paper for more details: https://arxiv.org/pdf/1102.1612.pdf https://arxiv.org/pdf/1102.1612.pdf (There are a few more technicalities which amount to forcing the simulator to solve an uncomputable puzzle before we tell them the laws. Let M be a turning machine that whose halting behaviour is undecidable. Even a spin-1/2 system might be "uncomputable" if all I tell you is that its Hamiltonian is (1 0; 0 1) if M halts and (1 0; 0 2) otherwise. Since a spin-1/2 system is one of the most blatantly computable things out there, this objection doesn't have much force.)