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In this article about the EMC effect (in no way relevant to my question), the statement is made:

The problem is that the complete QCD equations describing all the quarks in a nucleus are too difficult to solve, Cloët and Hen both said. Modern supercomputers are about 100 years away from being fast enough for the task, Cloët estimated. And even if supercomputers were fast enough today, the equations haven't advanced to the point where you could plug them into a computer, he said.

I want the simplest possible example of equations that can't be plugged into a computer (This really should go without saying, but I want an example that typifies the reason the QCD equations specifically can't be plugged into a computer. So I guess in some sense it is relevant to my question contrary to what I said above. Also if you want to talk about QCD or EMC that's fine; I wouldn't have read the article if I wasn't interested in those things, and maybe it's helpful in the context of the question as well?).

M.J. Rayburn
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This refers to a technical problem with lattice QCD simulations known as the "fermion sign problem", see also the previous post here. The sign problem implies that we can efficiently simulate the QCD equation of state at finite temperature, but not at finite net baryon density. We can compute the masses and properties of mesons and glueballs, but baryonic states with mass number $A>1$ are exponentially hard in $A$. The EMC problem refers to certain matrix elements in heavy nuclei (such as Calcium, $A=40$, or lead, $A=208$), which cannot be computed using available algorithms and computers architectures. It is conceivable that new classical algorithms, or new kinds of computers (quanutum) could help.

PM 2Ring
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Thomas
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Even with unlimited computational resources, a detailed solution of the QCD equations for a large number of interacting quarks is not possible because we do not have precise enough experimental values for some of the parameters involved. It is like trying to to solve $y=x+c$ when we only know that $c$ can take any value between one and a million. This means that numerical approximation techniques become unstable and run into problems like the numerical sign problem.

And the reason we do not have precise values for some of the parameters is that these values come from experiment, and some of the parameters require experiments at much higher energies than we can currently achieve.

gandalf61
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