DocumentCode :
2955869
Title :
Quantum versus Classical Proofs and Advice
Author :
Aaronson, Scott ; Kuperberg, Greg
Author_Institution :
Univ. of Waterloo, Waterloo
fYear :
2007
fDate :
13-16 June 2007
Firstpage :
115
Lastpage :
128
Abstract :
This paper studies whether quantum proofs are more powerful than classical proofs, or in complexity terms, whether QMA = QCMA. We prove three results about this question. First, we give a "quantum oracle separation" between QMA and QCM A. More concretely, we show that any quantum algorithm needs Omega (radic2n-m+1) queries to find an n-qubit "marked state" Psi rang, even if given an m-bit classical description of Psi rang together with a quantum black box that recognizes Psi rang. Second, we give an explicit QCMA protocol that nearly achieves this lower bound. Third, we show that, in the one previously-known case where quantum proofs seemed to provide an exponential advantage, classical proofs are basically just as powerful. In particular, Wa- trous gave a QM IK protocol for verifying non-membership infinite groups. Under plausible group-theoretic assumptions, we give a QCMA protocol for the same problem. Even with no assumptions, our protocol makes only poly-nomially many queries to the group oracle. We end with some conjectures about quantum versus classical oracles, and about the possibility of a classical oracle separation between QMA and QCMA.
Keywords :
quantum computing; theorem proving; classical proofs; quantum black box; quantum oracle separation; quantum proofs; Complexity theory; Computational complexity; Polynomials; Protocols;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Computational Complexity, 2007. CCC '07. Twenty-Second Annual IEEE Conference on
Conference_Location :
San Diego, CA
ISSN :
1093-0159
Print_ISBN :
0-7695-2780-9
Type :
conf
DOI :
10.1109/CCC.2007.27
Filename :
4262757
Link To Document :
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