This would be the place to start: https://arxiv.org/abs/1210.1847
An obvious constraint, then, is the quantization of spacetime and of all states. (You can't store an infinitely precise number. You are, however, allowed constants that you can evaluate to an arbitrary precision as needed. There will still be a rounding error.)
The number of interactions possible is likely too high for a simulation, so a simulation would take shortcuts, hierarchical simplifications so that you model objects as black boxes in black boxes rather than every quantum particle to every quantum particle.
This is speculative and harder to prove, but quantum foam is vast and there are something like a googol of each particle in the visible universe, which is just a segment of the full universe. Every pair of particles in all of this would need to be calculated for. Combinatorial explosion time, so simplification, so possible to break things.