English

Quantum vs Classical Proofs and Subset Verification

Quantum Physics 2018-06-29 v2 Computational Complexity

Abstract

We study the ability of efficient quantum verifiers to decide properties of exponentially large subsets given either a classical or quantum witness. We develop a general framework that can be used to prove that QCMA machines, with only classical witnesses, cannot verify certain properties of subsets given implicitly via an oracle. We use this framework to prove an oracle separation between QCMA and QMA using an "in-place" permutation oracle, making the first progress on this question since Aaronson and Kuperberg in 2007. We also use the framework to prove a particularly simple standard oracle separation between QCMA and AM.

Keywords

Cite

@article{arxiv.1510.06750,
  title  = {Quantum vs Classical Proofs and Subset Verification},
  author = {Bill Fefferman and Shelby Kimmel},
  journal= {arXiv preprint arXiv:1510.06750},
  year   = {2018}
}

Comments

23 pages, presentation and notation clarified, small errors fixed

R2 v1 2026-06-22T11:26:58.550Z