[adrian_b]

I am not sure what you mean by hydrogen.

QCD is about the strong forces, i.e. about the nucleus, which is a proton or a deuteron in the case of hydrogen.

However nobody has ever succeeded to make a useful simulation of the proton or of any other hadron.

Such a simulation must be based on a small number of universal parameters, e.g. the masses of the quarks etc., and it must be able to compute useful physical quantities, e.g. the masses of the hadrons, the magnetic moments of the hadrons, the energies of their excited states and so on, with a precision comparable with that of the empirical measurements.

Nobody has succeeded until now to perform such a simulation.

On the other hand, if we assign to the proton the properties determined by empirical measurements (i.e. mass and magnetic moment), quantum electrodynamics can be used to compute with high precision various properties of the proton-electron system, i.e. of the hydrogen atom.