Which cryptographic protocols are secure against quantum computer attacks? Are there any cryptosystems that we know that would be secure against an attack by a quantum computer?

Are there problems which are known or suspected to be hard for quantum computers, and can these be utilized to yield cryptographic protocols which are secure against quantum computers?
"Quantum Computers" may give you significant speedup in many types of attacks.
These speedups may not necessarily be exponential like the current Shor's algorithm usage for breaking RSA.
You may find more information here: https://security.stackexchange.com/questions/116596/will-quantum-computers-render-aes-obsolete