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Determining Acceptance Possibility for a Quantum Computation is Hard for the Polynomial Hierarchy

Stephen Fenner·Frederic Green·Steven Homer·Randall Pruim
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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 coC$_=$P.

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Stephen Fenner, Frederic Green, Steven Homer, Randall Pruim. 1998-12-18. Determining Acceptance Possibility for a Quantum Computation is Hard for the Polynomial Hierarchy. https://arxiv.org/abs/quant-ph/9812056

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