Crypto Snake Oil
On the topic of complexity classes ... Currently, the decision problem form of factorization is known to be in NP, co-NP, and BQP. Because it's within NP, it can not be NP-hard without being NP-complete. If it were shown to be NP-complete or co-NP-complete, that would imply that NP = co-NP, which is currently believed to to be false.
BQP is "bounded-error, quantum, polynomial" and represents what quantum computers are capable of. It is known to contain P and BPP, and to lie within PP and PSPACE.
Your claim that quantum computers should be able to solve NP-hard problems (presumably in polynomial time) doesn't make sense ...
I believe that your formulation of the problem, "any public key cryptosystem", makes it impossible to prove anything. I think you should at least make a list of problems that are currently used as the basis of various public key systems and start hacking at them ...
I'm sorry, but your post borders on incoherent, so it's difficult to comment on more of it.