English

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

Quantum Physics 2007-05-23 v3 Computational Complexity

Abstract

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.

Cite

@article{arxiv.quant-ph/9812032,
  title  = {NQP_{C} = co-C_{=}P},
  author = {Tomoyuki Yamakami and Andrew C. Yao},
  journal= {arXiv preprint arXiv:quant-ph/9812032},
  year   = {2007}
}

Comments

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