That's well done although two of the central premises are likely incorrect. First, the notion that a quantum computer would have infinite processing capability is incorrect. Quantum computation allows speed-ups of certain computational processes. Thus for example, Shor's algorithm allows us to factor integers quickly. But if our understanding of the laws of quantum mechanics is at all correct, this can't lead to anything like that in the story. In particular, under the standard descriptor for quantum computing, the class of problems reliably solvable on a quantum computer in polynomial time (that is the time required to solve is bounded above by a polynomial function of the length of the input sequence), BQP is is a subset of of PSPACE, the set of problems which can be solved on a classical computer using memory bounded by a polynomial of the space of the input. Our understanding of quantum mechanics would have to be very far off for this to be wrong.

Second, if our understanding of quantum mechanics is correct, there's a fundamentally random aspect to the laws of physics. Thus, we can't simply make a simulation and advance it ahead the way they do in this story and expect to get the same result.

Even if everything in the story was correct, I'm not at all convinced that things would settle down on a stable sequence as they do here. If your universe is infinite then your possible number of worlds are infinite so there's no reason you couldn't have a wandering sequence of worlds. Edit: Or for that matter, couldn't have branches if people simulate additional worlds with other laws of physics or the same laws but different starting conditions.