Quantum vs. Classical Proofs and Subset Verification

Authors Bill Fefferman, Shelby Kimmel

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Author Details

Bill Fefferman
  • Department of EECS, University of California at Berkeley, Berkeley, CA and, NIST, Gaithersburg, MD, USA
Shelby Kimmel
  • Department of Computer Science, Middlebury College, Middlebury, VT, USA

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Bill Fefferman and Shelby Kimmel. Quantum vs. Classical Proofs and Subset Verification. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 22:1-22:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum complexity theory
  • Theory of computation → Complexity classes
  • Quantum Complexity Theory
  • Quantum Proofs


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