Please an expert chime in to complement, but I believe simulation in quantum mechanics is a quite interesting and not so simple topic.
I believe the more correct thing to say is that quantum mechanics is approximable than simply computable. Don't forget, QM and current physical theories use real numbers, which are not digitally representable; although it seems also the case that information is locally bounded. The finite distribution of states and probabilistic dynamics is I believe is fundamentally what makes information bounded, (which forbids for example naive hypercomputation and I think several paradoxes that might arise from unbounded local information) but don't forget in general the dynamics is still based on continuous quantities as far as we know, not discrete quantities like in a computer. QM is about discrete states within a continuum set interacting with continuum dynamics, I think is accurate to say. Quantum field theory probably complicates things more but similar conclusions might be valid. This continuum dynamics can't be computed exactly, at most you could achieve a pretty good approximation; you'd also need to provision probabilities, either from pseudorandomness (which technically would invalidate the probabilistic model, although in practice this invalidation is not feasibly distinguishable by an observer of current human-scale computing power) or gathering environmental noise.
It's really interesting to me how nature is kind of surprising and defiant of simple hypothesis we come up with. But I think each of those characteristics plays a role, is an important part of existence somehow, and we should keep trying to understand why each aspect of nature is the particular way it is for their numerous insights into our condition and existence.