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The 7 faces of quantum NP
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When it comes to NP, its natural definition, its wide applicability across scientific disciplines, and its timeless relevance, the writing is on the wall: There can be only one. Quantum NP, on the other hand, is clearly the apple that fell far from the tree of NP. Two decades since the first definitions of quantum NP started rolling in, quantum complexity theorists face a stark reality: There's QMA, QCMA, QMA1, QMA(2), StoqMA, and NQP. In this article aimed at a general theoretical computer science audience, I survey these various definitions of quantum NP, their strengths and weaknesses, and why most of them, for better or worse, actually appear to fit naturally into the complexity zoo.
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Cited by 2 Pith 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.
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Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete
Unweighted gapped clique homology is QMA1^{g2}-complete for a fixed inverse-polynomial gap, proven by replacing vertex weights with clique multiplicities.
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