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