Quantum computers... what can they do better?

[eaglgenes101]

Suppose that in 20 years, the first general-purpose quantum processors for PC's are being sold. And naturally, wanting to see some speedups, I buy one of them and put it in my computer alongside regular hardware.

Assuming the software on my computer is designed to take advantage of quantum computing, what boosts would I notice? (Also assume that cryptographic standards have changed IE we're using NTRU instead of RSA, we're using 256-bit AES instead of 128-bit, 512-bit cryptographic hashes instead of 256-bit, etc., and we still don't know if P = NP.)

[OdinVanguard]

...snip... and we still don't know if P = NP.)

Kind of an important point there. If quantum computing can solve NP problems in P time thats gonna have  a pretty major impact.
Also, as best as I can gather, this could potentially render all current standard encryption models essentially obsolete because they would be too easy to crack... Most likely I think some form of quantum entanglement would be needed to really make things secure...
But I think its all speculation at this point.

...If nothing else, if they do get NP -> P then they can solve the traveling salesman problem in realtime and we all get to enjoy faster pizza delivery

[eaglgenes101]

Ok, by that I meant: suppose we don't have any way on hand of solving NP-complete problems in P time, classical or quantum.