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.
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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.