I'm under the impression that quantum computers buy you a square root. So instead of doubling the number of bits in your key to improve the strength of a key by

I'm under the impression that quantum computers buy you a square root. So instead of doubling the number of bits in your key to improve the strength of a key by a ludicrous amount, you should quadruple them. In addition to this, I don't know how well quantum computers help against (good) symmetric encryption. They help against certain types of PKI because they give you the aforementioned speedup in factoring large integers. However, I think Schneier's argument holds, because brute forcing 2^256 possible keys is.. well, see the argument above about forcing a counter through all those states. (apologies for not citing sources. Hopefully someone more knowledgeable can weigh in)