If you want to get pedantic we can't simulate anything with complete accuracy in the absence of a theory that encompasses all the known forces. Which we don't have. (Damn you gravity. Can't you just get along with the others)
replyTo a useful level of accuracy we can certainly simulate water. And we can do the same for a single proton for some definitions of useful (but not other definitions).
That's a fundamentally different problem and a terribly unfair comparison.
replyAm I right with my assumption that by "fundamentally different problem", you mean we lack a good simulation model, but that the number of degrees of freedom would actually be manageable?
replyTo simulate a proton you need to solve a strongly coupled highly relativistic SU(3) gauge theory (naturally non-abelian i.e. the force carrier field itself carries charge and is self-interacting at tree order) problem with constituents that have masses orders of magnitude below the relevant energy scales (i.e. you have many matter AND force particles that can pop in and out of existence and they all strongly interact with one another).
replyTo simulate a water molecule you do so with a weakly coupled SU(1) gauge theory (light does not interact with itself at tree order) problem where the masses of all constituents are orders of magnitude above the relevant energy scales (you can think of it as the electrons and nuclei and particles coming in and out of existence are contained in a renormalization scheme).
We have "good simulation models" of both, but the former is extraordinarily complicated compared to the latter for the reasons stated above.