“Wrong answers are not calculated” is a popular simplification of this, but it's misleading you here.
Quantum computers are a means of systematically creating and modifying complicated sums of exponentially large FFT's, and then efficiently sampling from the resulting distribution.
Note that you typically still need to sample many times to get a meaningful answer, which is where the “wrong answers are not calculated” ultimately comes from: if you can arrange for most or all of the factors corresponding to “wrong” answers in the sampled distribution to cancel out (such as the term for the number 4 when trying to factor 15), then when you sample several times from that distribution, very few or perhaps none of those samples will have been drawn from the “wrong” part of the distribution, and so you waste less time testing bad samples.
A quantum computer is potentially useful for simulating quantum systems because the _models_ for those systems are ridiculously complex in _exactly_ this way. It won't help if the model is wrong, but our problem is currently that we can't really run the calculations our current models imply beyond slightly-larger-than-toy examples.
How is this not “wrong answers are not calculated”? You gave a lot more detail on the mechanics of how these probability amplitudes are canceling each other out but the answer seems the same?
I don’t follow how this maps to helping simulate the quantum systems. Quantum computers are good at finding solutions to problems efficiently. But the quantum systems we are describing are not solution seeking systems. They’re going to be just interacting components with entanglement whatever’s going on. How would the avoidance of bad samples aid the simulation of a system like that?
But simulating a process is not the same thing as efficiently routing space exploration. Quantum computing grants you the latter. Why does it impact the former?
Quantum computers are a means of systematically creating and modifying complicated sums of exponentially large FFT's, and then efficiently sampling from the resulting distribution.
Note that you typically still need to sample many times to get a meaningful answer, which is where the “wrong answers are not calculated” ultimately comes from: if you can arrange for most or all of the factors corresponding to “wrong” answers in the sampled distribution to cancel out (such as the term for the number 4 when trying to factor 15), then when you sample several times from that distribution, very few or perhaps none of those samples will have been drawn from the “wrong” part of the distribution, and so you waste less time testing bad samples.
A quantum computer is potentially useful for simulating quantum systems because the _models_ for those systems are ridiculously complex in _exactly_ this way. It won't help if the model is wrong, but our problem is currently that we can't really run the calculations our current models imply beyond slightly-larger-than-toy examples.