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JoshuaZ comments on Theists are wrong; is theism? - Less Wrong
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If our understanding of the laws of physics is plausibly correct then you can't simulate our universe in our universe. Easiest version where you can't do this is in a finite universe, where you can't store more data in a subset of the universe than you can fit in the whole thing.
You could simulate every detail with a (huge) delay, assuming you have infinite time and that the actual universe doesn't become too "data-dense", so that you can always store the data describing a past state as part of future state.
That may not be a problem if the universe contains almost no information. In that case the universe could Quine itself... sort of.
If I'm reading that paper correctly, it is talking about information content. That's a distinct issue from simulating the universe which requires processing in a subset. It might be possible for someone to write down a complete mathematical description of the universe (i.e. initial conditions and then a time parameter from that point describing its subsequent evolution) but that doesn't mean one can actually compute useful things about it.
Sorry, but could you fix that link to go to the arXiv page rather than directly to the PDF?
Fixed.