As mentioned in a comment, 256-bit quantum security is overkill. Even AES-128 is unlikely to be broken by a quantum computer, as discussed here. Briefly: Grover's algorithm is the best possible; it doesn't parallelize efficiently; and it's unlikely that quantum computers will reach similar clock speeds as classical computers.
But assume you're really paranoid and want 256-bit quantum security anyway, so you'll need 512-bit classical security. You could either design a new 512-bit symmetric cipher, or use a composition of 256-bit symmetric ciphers. A similar situation had to be considered a few decades ago, when DES was standardized but AES didn't exist yet, and it became clear that 56 bits was within reach of motivated attackers, as concretely demonstrated by the EFF DES Cracker and distributed.net.
It turns out that, somewhat counterintuitively, double-DES does not have $2 \times 56 = 112$-bit security, but rather 57-bit security due to a very simple meet-in-the-middle attack. To achieve 112-bit security, triple-DES was required, and indeed was used in practice.
So, if you really want 512-bit classical security, you'd have to use triple-AES. In principle you could use only 2 different keys (although still using 3 chained encryption/decryption operations), but there exist attacks on that scenario, so for the truly paranoid, you'll have to use 3 different keys. Thus, a total of 768 bits of key material to achieve 512-bit classical security and 256-bit quantum security.
