How long does it take a quantum computer to brute force AES?
I'm not going to exactly answer your question, because I have no idea. I simply do not know how fast the quantum computer is that NSA is building in secret.

However I could explain why people recommend 256-bit security in the face of quantum computing using some numbers. If you feel that $2^{128}$ is a comfortable security against bruteforcing, remember that a $2^{64}$ security level is $18446744073709551616$ times faster to bruteforce. 

That means a ~0.000000000162630 GHz quantum processor bruteforces a 128 bit key faster than a 3GHz regular processor, assuming one lookup per cycle.