Adleman, DeMarrais, and Huang introduced the
nondeterministic quantum polynomial-time complexity class NQP as an
analogue of NQP. Fortnow and Rogers implicitly showed that, when the
amplitudes are rational numbers, NQP is contained in the complement of
C_{=}P. Fenner, Green, Homer, and Pruim improved this result by
showing that, when the amplitudes are arbitrary algebraic numbers, NQP
coincides with co-C_{=}P. In this paper we prove that, even when the
amplitudes are arbitrary complex numbers, NQP still remains identical
to co-C_{=}P. As an immediate corollary, BQP differs from NQP when the
amplitudes are unrestricted.

Adleman, DeMarrais, and Huang introduced the
nondeterministic quantum polynomial-time complexity class NQP as an
analogue of NP. Fortnow and Rogers showed that, when the amplitudes
are rational numbers, NQP is contained in the complement of
C_{=}P. Fenner, Green, Homer, and Pruim improved this result by
showing that, when the amplitudes are arbitrary algebraic numbers, NQP
coincides with co-C_{=}P. In this paper we prove that, even when the
amplitudes are arbitrary complex numbers, NQP still remains identical
to co-C_{=}P. As an immediate corollary, BQP differs from NQP when the
amplitudes are unrestricted.

Adleman, DeMarrais, and Huang introduced the
nondeterministic quantum polynomial-time complexity class NQP as an
analogue of NP. It is known that, with restricted amplitudes, NQP is
characterized in terms of the classical counting complexity class
C_{=}P. In this paper we prove that, with unrestricted amplitudes,
NQP indeed coincides with the complement of C_{=}P. As an immediate
corollary, with unrestricted amplitudes BQP differs from NQP.