Achieving perfect completeness in classical-witness quantum   Merlin-Arthur proof systems
  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. 
Stephen P. Jordan, Hirotada Kobayashi, Daniel Nagaj, and Harumichi   Nishimura
quant-ph