AWPP contains the complexity class BQP (bounded-error quantum polynomial time), which contains the decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances.
AWPP includes the complexity class BQP (quantum polynomial time with bounded errors), which comprises computational problems that can be solved by a quantum computer in polynomial time, with an acceptable level of error tolerance of up to 1/3 for every case.