It has been said -- I believe by Stephen Wolfram, who owes a very great deal to Zuse -- that the universe is "computationally irreducible." In other words, and particularly in this case, that every particle would need to be simulated by a similar particle or equivalent mathematical representation. And thus that any (quantum) computer running a simulation of our universe would need to be the size of the universe, and would require the energy of the entire universe.

In any case, the laws of physics are not yet settled, and determinism is still a very live option. The notion of a continuum is, to me, even more bizarre than the notion of a deterministic universe -- and is also more bizarre than Everett's notion of a "wave function of the universe."