[benkuykendall]

Yeah, we have some public key schemes that are conjectured to be resistant to quantum attacks. This one in particular is fun because of the connection to machine learning. (https://en.wikipedia.org/wiki/Learning_with_errors)

Basically, it uses the result that it should be 'hard' to learn a linear function with sufficient noise rate to create a cryptosystem.

[lkowalcz]

Also note that most homomorphic encryption schemes proposed so far are based on LWE and are therefore also conjectured to be resistant to quantum attacks.