Checking if a list is sorted is O(N) if you do it in a single thread since you'd have to check all the elements. If you can do it with a prefix sum or something, it should be possible to do it in O(log N) over many cores.

Btw, the quantum bogosort also assumes that destroying the universe is O(1), which seems unlikely. Clearly, when sorting a bigger list there is more information in the universe (ie the list). Since information and energy seem to have some equivalence in quantum dynamics, is does not seem unreasonable that destroying a universe with more information in it would take longer and so destroying the universe cannot be O(1).