License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2018.22
URN: urn:nbn:de:0030-drops-96040
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9604/
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Fefferman, Bill ; Kimmel, Shelby

Quantum vs. Classical Proofs and Subset Verification

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LIPIcs-MFCS-2018-22.pdf (0.6 MB)

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 [Aaronson and Kuperberg, 2007]. We also use the framework to prove a particularly simple standard oracle separation between QCMA and AM.

BibTeX - Entry

@InProceedings{fefferman_et_al:LIPIcs:2018:9604,
  author =	{Bill Fefferman and Shelby Kimmel},
  title =	{{Quantum vs. Classical Proofs and Subset Verification}},
  booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
  pages =	{22:1--22:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9604},
  URN =		{urn:nbn:de:0030-drops-96040},
  doi =		{10.4230/LIPIcs.MFCS.2018.22},
  annote =	{Keywords: Quantum Complexity Theory, Quantum Proofs}
}

Keywords: Quantum Complexity Theory, Quantum Proofs
Collection: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 27.08.2018

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