Well, if they do come up with a working, functionally complete quantum computer SHA256 calculations become trivial. I don't expect we'll have one any less than 20 years from now. They've only just barely got the first hybrid quantum chips working. I'd love to be wrong though, there are a lot of things we could do with quantum computers that current digital computers suck at.

ASICs will probably get better, especially if fabbed at smaller processes but quantum computers change the game enough that an SHA or scrypt-based Bitcoin would likely not survive. Quantum computers would change the field of cryptography significantly. Because these algorithms are all based on the sums of large primes Shor's algorithm could be used to solve them vast orders of magnitude faster than current computers. Fast enough that one system could conceivably calculate out any and all possible answers fairly quickly. That's just simple COMPSCI 101 stuff.

Sounds like your Compsci 101 failed you. Shor's Algo will not break hashing algo's like SHA, Grover's will. Shors will break ECDSA (bitcoin signing) by solving the ECDLP. I don't expect someone in Compsci 101 to know all of that though.