In any case, here’s some food for thought: ray tracing is undecidable [1]. If something is undecidable, it is for any form of computation, classical, quantum, or anything. Does this mean we can find some “glitches in the matrix”. It simply means such glitches are there (if we are in a similation). But they might be too infinitesimal for us to identify.
[1]https://users.cs.duke.edu/~reif/paper/tygar/raytracing.pdf
Does it? Do they?
Yes. The halting theorem is a version of God's omnipotence paradox: if God is omnipotent, can he make a rock that's so heavy that he can't lift it? Either way, God's power is limited. Similarly, can God create a universal halting decider? If he can, then we can use that halting decider to create a program whose halting can't be decided. I won't bore you with the details, but the idea is that the "God" I used above can be anything. It can be the writers of the simulation we live in.
> Do they?
No matter who the writers of the simulation are, they are finite beings, and their devices are finite, one way or another. The set of real numbers is infinite and uncountable. So not all numbers can be represented. Any representation of real numbers will make approximations.