One correction Bitcoin does not utilize RSA.  
It uses SHA-256, RIPEMD-160, and ECDSA (specifically the secp256k1 curve).  The satoshi wallet also uses SHA-512 & AES but that is client side (encrypted private keys) and not part of the protocol.

Bitcoin by nature will never employ quantum cryptography.  Quantum cryptography requires a direct (no relay) communication link in order to exploit the quantum properties which make it possible.  By direct I mean something like a single fiber optic cable (without any amps, relays, or switches) between a single sender and a single receiver.