[pdpi]

"Solve problem x in polynomial time". AIUI, BQP is thought to be a superset of P and to include some stuff from outside NP. Specific problems that are part of BQP but that we expect are not in P is the interesting response here.

An example of such a problem is integer factorisation (see: Shor's Algorithm), which means that RSA and similar schemes might become vulnerable once suitably large quantum computers are available.