Determining acceptance possibility for a quantum computation is hard for the polynomial hierarchy

It is shown that determining whether a quantum computation has a non-zero p robability of accepting is at least as hard as the polynomial-time hierarch y. This hardness result also applies to determining in general whether a gi ven quantum basis state appears with non-zero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end o f a quantum computation. This result is achieved by showing that the comple xity class NQP (a quantum analogue of NP) of Adleman, Demarrais and Huang i s equal to the counting class coC(=)P.