We always hear about the ramifications a quantum computer would have if used to crack enterprise level security. Does there exist encryption that would be troublesome even for a quantum computer to crack or are we just SOL if one of these falls into the wrong hands?
Lattice-based cryptography (https://en.wikipedia.org/wiki/Lattice-based_cryptography) is currently believed to be quantum-computer resistant (i.e. requires super-polynomial time to break even on a sufficiently large quantum computer).
There are only very few problems were quantum computers achieve an exponential speedup vs. classical computers, factoring being one example.
It's a little pricey (I think it's meant as a textbook), but DJB has a book on post-quantum cryptography‡
He also has an intro paper (which is probably more along the lines of what you're looking for)‡
Hash-based cryptography, code-based cryptography, lattice-based cryptography, and multivariate-quadratic-equations cryptography are all methods that should hold up in a post-quantum world.
I believe that quantum computers only give a square root speedup for bruteforcing symmetric encryption algorithms, so we'd just have to double the key length of those.
Asymmetric algorithms based on the hardness of factoring or calculating discrete logarithms are broken, though.
