O erro mais comum é achar que um computador quântico resolve um problema NP-completo em tempo polinomial, o que não é verdade.

(perdoem-me o dupe)

http://scottaaronson.com/blog/?p=198
Q: But couldn’t quantum computers try all possible solutions in parallel, and thereby solve NP-complete problems in a heartbeat?

A: Yes, if the heart in question was beating exponentially slowly.

Otherwise, no. Contrary to widespread misconception, a quantum computer could not “try all possible solutions in parallel” in the sense most people mean by this. In particular, while quantum computers would apparently provide dramatic speedups for a few “structured” problems (such as factoring integers and simulating physical systems), it’s conjectured that they couldn’t solve NP-complete problems in polynomial time.

Q: But isn’t factoring an NP-complete problem?

A: Good heavens, no! While factoring is believed to be intractable for classical computers, it’s not NP-complete, unless some exceedingly unlikely things happen in complexity theory. Where did you get the idea that factoring was NP-complete? (Now I know how Richard Dawkins must feel when someone asks him to explain, again, how “life could have arisen by chance.”)

Outro engano é achar que um computador quântico tornaria todas as técnicas de criptografia inúteis:

Several groups are working on designing and building a quantum computer, which is fundamentally different from a classical computer. If one were built — and we’re talking science fiction here — then it could factor numbers and solve discrete-logarithm problems very quickly. In other words, it could break all of our commonly used public-key algorithms. For symmetric cryptography it’s not that dire: A quantum computer would effectively halve the key length, so that a 256-bit key would be only as secure as a 128-bit key today. Pretty serious stuff, but years away from being practical.

http://www.schneier.com/blog/archives/2009/09/quantum_compute.html