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I know that a Turing machine^{1} can theoretically simulate "anything", but I don't know whether it could simulate something as fundamentally different as a quantum-based computer. Are there any attempts to do this, or has anybody proved it possible/not possible?

I've googled around, but I'm not an expert on this topic, so I'm not sure where to look. I've found the Wikipedia article on quantum Turing machine, but I'm not certain how exactly it differs from a classical TM. I also found the paper *Deutsch's Universal Quantum Turing Machine*, by
W. Fouché et al., but it is rather difficult to understand for me.

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1. In case it is not clear, by Turing machine I mean the theoretical concept, not a physical machine (i.e. an implementation of the theoretical concept).}

1"Randomness = ignorance" is a very deep misunderstanding. It boils down to uncertainty principle and noncommutativeness of observables. ONLY in a quantum setting you can have an experiment, in which the outcome cannot be predicted EVEN IN PRINCIPLE, - the quantum measurement. No classical random generator can capture this feature of a quantum computer. But the current terminology is such that neither weak nor strong definitions of simulation require this, so, technically speaking, we can simulate a quantum computer classically, even though the final randomness will not be quantumly random. – mavzolej – 2020-09-24T05:19:52.747

@mavzolej: I think you're taking current theories a tad too literally, coming to a quantum-mysticism sort of view. That said, at current we can't prove that Quantum Mechanics doesn't emerge from a deeper deterministic theory. Sure such a theory might be stupidly complex; sure it might be non-local or/and retro-causative, but it could exist. Given that we can't exclude the possibility of determinism, what sense does it make to assert fundamental quantum randomness as anything more than a feature of the current theory? – Nat – 2020-09-24T19:14:56.557

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You're talking now about hidden variables , this possibility has been studied thoroughly and eliminated.

– mavzolej – 2020-09-24T21:12:48.710@mavzolej: Are you referring to Bell experiments for local hidden variables? Because deterministic generalizations have not been eliminated; nor could they be, even in theory. (Well, in

extremetheoretical contexts, the question gets interesting. But, practically speaking.) – Nat – 2020-09-24T21:15:24.787