Achieving perfect completeness in classical-witness quantum Merlin-Arthur proof systems

TL;DR

This paper demonstrates that classical-witness quantum Merlin-Arthur proof systems can be modified to always accept valid proofs, achieving perfect completeness under certain gate sets, using a novel quantum technique.

Contribution

It proves QCMA equals QCMA1 under specific gate sets, introducing a new quantum method to adjust success probabilities additively.

Findings

QCMA equals QCMA1 under certain gate sets

Introduces a quantum technique for success probability adjustment

Proof is nonrelativizing and broadly applicable

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.