I'm not aware of any data that says either that the brain relies on quantum effects, that quantum effects are needed to solve the binding problem, or even for sure that the binding problem is a problem that needs solving.
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.
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
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.
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.
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)”
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.
Your left and right visual fields are united in one "space". Classical computation cannot achieve such unity. Digital computation concerns discrete parts changing in discrete steps, which is not like a field at all.
Sure they can, self driving cars do it with a half dozen or more visual fields combining to a single model of the world around them.
Also, your visual system is fairly discrete, between the receptive fields of individual retinal cells, to the granularity of the optic nerves, to how the bottom end of the visual cortex samples all of that.
Self-driving cars don't experience visual qualia. A model is not the same as an actual experience. There's no binding-problem to solve with self-driving cars because there's no attempts to make them conscious. It's a completely different thing.
There's no reason to believe qualia arise in a given discrete computation. Why would they? In what steps in the algorithm do qualia arise and why, what characteristics do they have, what causal roles do they play, etc.
It's completely self-evident we experience qualia. It's what our experiences are made of. There wouldn't be anything to experience or discuss if we didn't. The brain is not a deliberate, man-made object like a computer is, hence why it can possess these properties with us being unaware of how (they were selected for via evolution), but the computer cannot.
The input system is discrete but the end-result, our conscious experience of our world-simulations (made up of visual qualia) are not discrete. They are unified.
An example of how this could be implemented (not saying this is the case, just one of several possibilities):
But that whole argument comes from the a priori idea that you can't build a singular model of the world from discrete inputs. There's no evidence or even logical chain for that conclusion.
And even the quantum world is discrete. That's why it's called a 'quantum'. There are fixed size quantities moving through the field.