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Are arbitrarily good approximations of the time evolution of any QCD system, given initial and boundary conditions, Turing computable? Can lattice QCD simulations be used to do so in theory?

How close are we to proving or disproving the computability of QCD systems?

If it is known that QCD is computable, do we know anything about its computational complexity?

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    $\begingroup$ I don't know so much about formal computability, but I can mention that lattice QCD calculations don't access time evolution; they only give equilibrium expectation values from the functional integral. I am aware of an argument that massive scalar field theory in 1+1 space-time dimensions is BQP-complete, and would expect (3+1)d QCD to be at least as hard. $\endgroup$ – David Schaich Aug 24 '19 at 11:43

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