How resistant are stream ciphers like Salsa20 or ChaCha in a post-quantum world? What kind of quantum computer would be required, if it is possible to break such ciphers?
There is no known quantum attack better than the generic Grover attack on Salsa20 and ChaCha, which is inconsequential because it would take $2^{128}$ sequential steps.  Even if parallelized $p$ ways to run in marginally less time, a factor of $\sqrt p$ improvement, it would cost more, also by a factor of $\sqrt p$, than the cost to run a quantum computer for $2^{128}$ steps.  Even if you were satisfied with breaking the first of $t$ targets for $t \ll p$, you would get only a $\sqrt[4] t$ cost reduction in the best known multi-target attack.

The same is true for AES key recovery, SHA-256 preimage search, etc.  More on quantum attacks on various kinds of hash functions.