[throwaway81523]

No I don't see how to implement QM as a computer program while preserving basic complexity invariants of Turing machines. That is the point of quantum computing: that the complexity classes for quantum computers are different than those for Turing machines. If you take the view that that the whole Universe is one gigantic entangled quantum state, the cellular automaton simulation would get pretty bogged down.

[tsimionescu]

Quantum Computers are no more powerful than Turing Machines, complexity has little to do with this. Quantum Mechanics, being a linear theory (if we exclude measurement) is actually relatively easy to describe computationally. The computations are incredibly slow, but otherwise they are perfectly in line with any other formulation of the theory.

[throwaway81523]

> Quantum Computers are no more powerful than Turing Machines

They are more powerful in the sense that P-time for quantum computers (aka BQP) is hypothesized to be larger than P-time for Turing machines. That is different from every classical model of computation (RAM machines, etc.) that we usually talk about. It's hard to call something a cellular automaton if it has to expand exponentially in size as it evolves. Thus, 't Hooft concretely predicts that if his CA model is right, then quantum computers can't work. Idk whether Wolfram addresses this issue.

[whimsicalism]

You are conflating multiple unrelated issues.