Quantum computers can use Shor’s algorithm to break the main public key cryptosystems. Those based on the difficulty of factoring and the discrete logarithm, but there are still public key cryptosystems which are so far resistent to both quantum and classical attacks (like those based on certain shortest vector in a lattice problems.) Quantum computers can’t break any code in existence.
More discussion of encryption vulnerability to Shor Algorithm and Grover's algorithm (using QC to speed up database searches)
Public Cryptography is discussed at SSH
Symmetric cyphers are discussed at SSH
Elliptic curve cryptography at wikipedia.
The Case for Elliptic Curve Cryptography at the NSA.
A list of different kinds of attacks on Cryptographic systems. Article by SSH