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.

I assume that we are talking about situations where public key cryptography is used.

If you share one master key for long time, having (effectively) 128-bit secret shared state is too small.