eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-27
22:1
22:23
10.4230/LIPIcs.MFCS.2018.22
article
Quantum vs. Classical Proofs and Subset Verification
Fefferman, Bill
1
Kimmel, Shelby
2
Department of EECS, University of California at Berkeley, Berkeley, CA and, NIST, Gaithersburg, MD, USA
Department of Computer Science, Middlebury College, Middlebury, VT, USA
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 [Aaronson and Kuperberg, 2007]. We also use the framework to prove a particularly simple standard oracle separation between QCMA and AM.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol117-mfcs2018/LIPIcs.MFCS.2018.22/LIPIcs.MFCS.2018.22.pdf
Quantum Complexity Theory
Quantum Proofs