David Tong and Lubos Motl have argued that our universe can't possibly be a digital computer simulation because chiral gauge theories can't be discretized, and the Standard Model is a chiral gauge theory. Certainly, you can't regulate them on a lattice. However, that doesn't mean they're not limit computable. There are only two alternatives. Either chiral gauge theories are uncomputable (extremely unlikely), or they can be simulated on a digital computer. How do you simulate a chiral gauge theory on a digital computer? Attempts by Erich Poppitz have fallen a bit short of the goal.
Overlap fermion approach may be the answer. Ounce a theory is defined on a lattice, it can be simulated by a computer that we already have. Here is a review on overlap fermion approach:
Tata lectures on overlap fermions arXiv:1103.4588
Overlap formalism deals with the construction of chiral gauge theories on the lattice. These set of lectures provide a pedagogical introduction to the subject with emphasis on chiral anomalies and gauge field topology. Subtleties associated with the generating functional for gauge theories coupled to chiral fermions are discussed.
==== A new result ===
One can simulate any anomaly-free chiral gauge theories on a computer by simply put it on lattice and turn on a proper interaction. See my new papers http://arxiv.org/abs/1305.1045 and http://arxiv.org/abs/1303.1803