From a talk by D. J. Bernstein http://cr.yp.to/talks/2008.10.18/slides.pdf :
ECC in general: Dead.
HECC in general: Dead.
Class groups in general: Dead.
Example: 1979 Merkle hash-tree public-key signature system.
Example: 1978 McEliece hidden-Goppa-code public-key encryption system.
Example: 1998 “NTRU.”
Example: 1996 Patarin “HFE^V-” public-key signature system.
Example: 1998 Daemen–Rijmen “Rijndael” cipher, aka “AES"
At its core, to do public-key cryptography, you just need a difficult instance of an NP-but-non-P problem. Quantum computers put factorization and discrete logarithms into P, but there are still plenty of harder NP problems that have not been tapped. If quantum computing starts to become a significant threat, we'll probably see renewed interest in those.
Maybe I'm misunderstanding but if you had one of these you would have answered a fairly important question in CS theory. Perhaps you mean to say "NP-complete", but even then I'm not sure the proposition is correct.
Or, better, any practical implementation of quantum cryptography is succeptible to attacks. And the entire thing still needs an authentication method, guess what we use for authentication nowadays.
The #1 advantage of QKD is not that the methods being used today will be immune to all attacks found in the future. It's that quantum states are unclonable, so there's no way to archive cipher-text for future attacks, as can be done with classically encrypted messages. e.g. If you send encrypt a message and send it via email today, the encryption method has to stand up to advances in algorithms and computational hardware for as long as the information remains sensitive. If you send something via QKD, an eavesdropper must break the protocol at the moment you send the message or it will be safe for all time.
Authenticating strangers, as in credit card transactions, is something that quantum computing may disrupt. QKD can be used safely by people who have met at some point in the past, but we probably have a bit of time before CC transactions need to be encrypted by QKD. i.e. While you should probably not send medical records or state secrets via many classical encryption protocols now, your CC info will change in a couple years so it's not as big of an issue if your transactions are cracked a few years after that.
Many key exchange protocols treat the asymmetric operations as black boxes, so you can replace RSA with any other asymmetric cipher.