The complexity class BQP (bounded-error quantum polynomial) is not widely believed to contain NP-complete problems. Instead, if it is indeed different from BPP,

The complexity class BQP (bounded-error quantum polynomial) is not widely believed to contain NP-complete problems. Instead, if it is indeed different from BPP, it probably contains problems between P and NP, which we know to exist (so long as P!=NP).