How would quantum computers affect password based encryption? At first glance: Assuming that the output of the password hashing function is large enough, 
quantum computers should have no effect on password encryption as on symmetric cryptography in general. 
Is that correct?  

More precisely: Grover's search invokes an oracle instead of searching a dataset. Does this mean that 
dictionary attacks cannot be performed efficiently with quantum computers?
Is there any other way in which quantum computers could be used for password cracking?
Currently we use slow key derivation functions. If a hypothetical quantom computer could run these as fast as a classical computer (Which is a huge If) grover's algorithm would allow searching over the equivalent of the squared root of the password space.
However even a sizeable quantom computer won't be able to do that. We will be seeing Shor's algorithm being used to attack RSA and DH before we see Grover's used to attack old 128 bit encryption. And that before it will be used against a password based key derivation function.
And I expect none of this soon.