Quantum mechanics, because it's a matter of probabilities, however, would re-roll the dice (so to speak) each time you had an interaction, and so any given calculation would diverge from the previous barring a statistical fluke of astronomic proportions.
I must admit that I'm still of the opinion that below the available resolution of measurement (Planck-distance/time) there's a fully deterministic system that remains hidden to us but means that the seemingly strange dice-throws would always
be those same seemingly strange dice-throws. And to a GUT that is worthy of the title (and a probably impossible amount of information, of course) things like wave/particle dualities, slit experiments, quantum tunnelling, etc, etc are.
Of course, even if we knew what we needed to know, it'd be easier at low levels just to work on the probabilistic methods that we have (or shall continue to develop), entirely from QM, just as we deal with reletivistic.
I consider it a point of failure that I am so melded to the Deterministic/Hidden Variable view of the universe, for I know it might not be, but I just prefer a certain type of elegance in it. And, so far, have not fully understood (or, rather, accepted) an apparent proof against this worldview that a certain experiment was supposed to have provided.
I also have this thing about looking for a PRNG that (in common with the Universe) is fully capable of giving the situation that a coin-toss comes up heads 100 times in a row, albeit so rarely... of course, for this to be possible (and yet not certain) in the same ratio as Real Life, it needs to be a PRNG with an internal state having vastly more than 2
100 possible values through which to cycle in order to accommodate both this sequence and every other possible sequence of equal length at some point in its Pseudorandomness. But that's more Information Theory than Physics, I put it here just as another example of my inane idealisms.