In practice schemes based on cryptographic hash functions work just as well and are quantum resistant. 512-bit key length is safe from quantum computers. Use bcrypt, Argon2 if you are pessimistic.
Using side channel to share single 512-bit key that is used to generate other keys keys is enough.
The best known quantum attack against symmetric ciphers uses Grover's algorithm to effectively halve the key size. AES-128 is considered secure against classical attacks, so assuming you have a secure side channel for key distribution, AES-256 is sufficient to defeat quantum attacks.
Using side channel to share single 512-bit key that is used to generate other keys keys is enough.