Achieving perfect completeness in classical-witness quantum merlin-arthur proof systems

Authors:
Stephen P. Jordan;Hirotada Kobayashi;Daniel Nagaj;Harumichi Nishimura
Affiliations:
Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD and California Institute of Technology, Pasadena, CA;Principles of Informatics Research Division, National Institute of Informatics, Tokyo, Japan;Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia;Graduate School of Science, Osaka Prefecture University, Sakai, Osaka, Japan
Venue:
Quantum Information & Computation
Year:
2012

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Abstract

This paper proves that classical-witness quantum Merlin-Arthur proof systems can achieve perfect completeness. That is, QCMA = QCMA1. This holds under any gate set with which the Hadamard and arbitrary classical reversible transformations can be exactly implemented, e.g., {Hadamard, Toffoli, NOT}. The proof is quantumly nonrelativizing, and uses a simple but novel quantum technique that additively adjusts the success probability, which may be of independent interest.