It is probably best for you to stay away from the physics/QM point of view on this, since you will lose: the states "between the computational elements", whatever you may mean by that, decohere and relax to "thermal noise" much quicker than the time between clock transitions, so there no difference between a nanosecond an an hour.

Maybe what you mean is more logic-related?...

No, I meant the physical explanation (I am a physicist, btw). It is possible for a system to exhibit features at certain frequencies, whilst only showing noise at others. Think standing waves, for example.

I agree that forking a consciousness is not a morally trivial issue, but that's different from temporary suspension and restarting, which happens all the time to people and machines. I don't think that conflating the two is helpful.

When does it ever happen to people? When does your brain, even just regions ever stop functioning, entirely? You do not remember deep sleep because you are not forming memories, not because your brain has stopped functioning. What else could you be talking about?