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

@article{Fenner1998DeterminingAP,
  title={Determining Acceptance Possibility for a Quantum Computation is Hard for the Polynomial Hierarchy},
  author={Stephen A. Fenner and Frederic Green and Steven Homer and Randall Pruim},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={1998},
  volume={6}
}
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 [1… CONTINUE READING

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