Is there a reason that you are interested in QED in particular? For processes within current experimental ranges, the standard perturbative treatment is incredibly accurate, and simulations are not really necessary.
A sector of the standard model where simulations are incredibly important is in strong interactions (QCD) for which a perturbative treatment is not satisfactory as one heads to the IR (low energy). A good reference to start at could be: http://arxiv.org/abs/hep-lat/0506036
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