With an infinite counter register as part of the witness, QMA and its perfect-completeness variant QMA_1 become the same complexity class, and a finite truncation gives doubly-exponential completeness amplification.
Achieving perfect completeness in classical-witness quantum Merlin-Arthur proof systems
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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.
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quant-ph 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
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${\sf QMA}={\sf QMA}_1$ with an infinite counter
With an infinite counter register as part of the witness, QMA and its perfect-completeness variant QMA_1 become the same complexity class, and a finite truncation gives doubly-exponential completeness amplification.