[robotresearcher]

I also know of no such data, and only arguments that are not commonly accepted. Anyhow, what prevents a TM simulating a system 'at the quantum level'? A TM has infinite storage by definition, so the state space is not a limiter.

[ZeroFries]

Lots of reasons. You need energy to store the information. You wouldn't be gaining anything, only losing efficiency. The quantum level is the "lowest" level of existence, there's nothing "lower" to use to simulate it. Furthermore, "random" is a critical concept in QM, and one can never achieve true random with a TM. What's the digital algorithm to generate a truly random number?

Edit: in a way simulating a crab with a bunch of crabs would be kind of like simulating energy dynamics/QM with energy

[drdeca]

A Turing machine, that is, the mathematical formalism, can definitely simulate quantum mechanics. A classical Turing machine simulating a quantum Turing machine, or other model of quantum computation, would, aiui, incur a super-polynomial slowdown (maybe exponential? My impression is that that it might not be known to exponential. But at worst basically exponential).

The randomness is not an issue. Just don’t add any wave function collapse, or just list the probability of each outcome.

[ZeroFries]

This is just not the case, even with infinite energy and time. There are properties of quantum Turing machines that are not reproducible with classical Turing machines.

https://web.archive.org/web/20081123183419/http://www.ceid.u...

[drdeca]

That abstract appears to be referring to the superpolynomial slowdown in simulating one, which I already pointed out.

(If there is more than the abstract there, the scrolling isn’t working on my phone.)

There is no function that a QTM can compute that a TM cannot. But a QTM can compute some functions much faster.

Or, as phrased in the abstract “these do not include the computation of any non-recursive function”.

Edit: of course, there are things that can can be done with QM that can’t be with a TM (such as the entangled multi-party prover/verifier setup), but none of them are “compute this function (with no limit on how long it takes)” or “simulate this situation (with no limit on how long it takes)”

[ineedasername]

Quantum may not be the lowest level: Nobel prize winning physicist Gerard 't Hooft speculates the existence of a more orderly layer underlying the quantum layer.

Otherwise, I see no reason why a thing cannot be used to simulate a thing of the same kind: Computers are used to simulate other computers on a daily basis.

[numpad0]

Do something nondeterministic qualify as a simulation