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JGWeissman comments on Open Thread: September 2009 - Less Wrong
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Quantum computers are computers which use quantum superposition for parallel processing, and are not required for simulating quantum mechanics. And our "classical" computers do in fact take advantage of quantum mechanics, as classical physics does not allow for solid state transistors.
It seems that quantum computers are required for simulating quantum mechanics in sub-exponential time, though.
When discussing asymptotic algorithmic complexity, you should specify the varying parameter of problem complexity.
The usual default parameter is number of bits it takes to write down the problem. It could also be number of particles. Either one works in this case.
What quantum algorithm for simulating quantum mechanics takes sub-exponential time with respect to the number of particles?
I didn't have a particular algorithm in mind when I said that, but since you ask I went and found this one.