Determining Acceptance Possibility for a Quantum Computation is Hard for the Polynomial Hierarchy
Quantum Physics
2007-05-23 v1
Abstract
It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end of a quantum computation. This result is achieved by showing that the complexity class NQP of Adleman, Demarrais, and Huang, a quantum analog of NP, is equal to the counting class coCP.
Cite
@article{arxiv.quant-ph/9812056,
title = {Determining Acceptance Possibility for a Quantum Computation is Hard for the Polynomial Hierarchy},
author = {Stephen Fenner and Frederic Green and Steven Homer and Randall Pruim},
journal= {arXiv preprint arXiv:quant-ph/9812056},
year = {2007}
}