NQP_{C} = co-C_{=}P

Details NQP_{C} = co-C_{=}P NQP_{C} = co-C_{=}P

1998-12-14

arxiv.org/abs/quant-ph/9812032v3

Inform.Proc.Lett. 71 (1999) 63-69

Physics

Quantum Physics

9 pages. Accepted for Information Processing Letters, June, 1999

Scientific paper

Adleman, DeMarrais, and Huang introduced the nondeterministic quantum polynomial-time complexity class NQP as an analogue of NP. 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.

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