If we define consciousness as just "awareness" in general, which is admittedly a vague definition, then consciousness persists as long as we are awake. If your definition includes thought processes as distinct elements of consciousness, then the states do correspond to physical states; they are the physical state of the brain. With a better definition of consciousness we could more easily dissolve the question, but until you do that we don't know what question we're trying to dissolve.

If one's consciousness suddenly became a totally different one, we know of know quantum particles that would change.

Changing someone's personality would cause many changes to the brain, since the functioning of the brain is responsible for it. If by this you mean their "identity" changes rather than any actual measurable physical or mental characteristics, then what do you mean by identity? Does it correspond to anything in reality?

This reminds me of the "why am I me and not somebody else" question, the answer to which is that "you" are the result of a mind growing up in that particular body/environment, and "you" can't have grown up in a different body because a mind growing up in a different body would be a different mind. There's no mystical identity that can transfer between people or through time (which I think is what you were actually trying to prove in your post, and which requires further argument to prove).

Swapping consciousnesses would make no changes to what is percieved.

Again, what do you mean by consciousness; a person's mind or some sort of "identity"? There are entire movies whose premises are based on swapping minds and the very apparent changes that result.

E.g. if one agent perceives p and time t and p' at the next time t+1, and another agent perceives q at time t and q' at time t+1, then if their consciousnesses are "swapped," the percepts would still be identical: p and q will be perceived at time t, and p' and q' will be perceived at t+1.

Then what are we swapping? If I swap subject p's brain with subject q's, then how can I call the consciousness currently in q's body q?

I agree that reasoning along lines similar to this can lead one to reject the concept of numerical identity of consciousness, but one needs to define what they mean by consciousness first. If you are thinking more along the lines of identity rather than consciousness per se, there's a lot of information about the diachronic problem.