Why must computer models use the classical model? Isn't it possible to encode what we know about quantum mechanics in a simulation and see what comes of it?
Consider a shaped piece of glass. It "calculates" something about how a light-input bounces, is diffused, makes interference patterns, etc. It leverages natural laws directly and quickly, literally at the speed of light. Perhaps with the right shape and the right light-beam, we can answer questions that matter to us.
Now imagine a programmed version, where all those calculations that "just happen because the universe works that way" have to be done by a CPU crunching numbers. (Ultimately relying on its own set of natural laws.) The second case is going to be much slower.
Another analogy might be a bunch of gear-based clockmakers who want to use electronic circuits instead... A gear-based simulation of electrons doesn't really help them.
That makes sense. However if the classical computer were strategically directed to the corners of the [search] space that are interesting, maybe interesting results could arise. It would be hard to have any sort of confidence in those I suppose if it must ignore large swaths of the space, however. It may serve as a discovery process informing more refined experiments though.
Also, as I mentioned to another replier, I didn't say which type of computer must be used-- it should be possible with a quantum computer running software rewriting the NP-hard problem in terms most natural [i.e., native] to it. :-)
Also, I was thinking more along the lines of using randomness + probabilistic models to shortcut the actual calculations involved. Since quantum mechanics already involves a lot of probability (to which depth we don't really understand yet), it seems that this should be feasible.
Quantum physics is completely deterministic until you perform a measurement - no randomness involved. And the randomness associated with measurements may be just due to our ignorance.
Quantum physics is - in some sense - strictly more complex than classical physics and therefore simulating quantum physical systems with classical systems, for example a classical computer, causes exponentially growing costs. Besides that quantum physics is non-local and can not be simulated at all if you have only access to local state. There is a prize of a million dollar waiting for you if you can demonstrate the opposite [1].
Well, I didn't specify what type of computer must be used. :-) It should be possible with a quantum computer, yea? Then it merely becomes rewriting one NP-hard problem in terms of another one (one being related to the refraction of light in glass and the other being whatever basis the quantum computer is built in terms of).
Also, are you sure that the Copenhagen interpretation is correct? Aren't 'local hidden variable theory' and 'consistent histories theory' also possible?
Yes, quantum computers can efficiently simulate quantum systems, it is really very much like the situation with NP-complete or NP-hard problems. [1]
As far as we know and if we did not miss a loophole, the violation of Bell's inequality force us to give up locality, realism or freedom. So you can keep locality if you throw realism or freedom over board. But this will (probably) not help winning the money in practice.
No, not really. There are many reasons. One, the outcomes for quantum theory computations have counterintuitive properties, like entanglement and the observer effect. Two, computations to predict quantum outcomes for aspects we do understand are very difficult. As one example, we can model a hydrogen atom and predict its spectral lines, but any more complex atoms are beyond computational prediction. This is true in spite of the fact that, in principle, we can say what rules and equations should be applied.
The tl;dr: quantum theory computations are very complex and become more complex very quickly.
Quantum systems can be simulated by classical computers, but the growth of the problem is exponential. If you can leverage actual quantum systems to do the work, then you can take a shortcut, for certain classes of problems.
> In a way, it is like answering questions about airplane design by studying a model airplane in a wind tunnel – solving problems with a physical simulation rather than a digital computer.
