QMA has perfect completeness

Abstract:We prove $\mathsf{QMA} = \mathsf{QMA_1}$, i.e., every quantum Merlin-Arthur proof system can be made perfectly complete. Our construction uses only Hadamard, Toffoli, and $X$ gates, yielding a universal gate set for $\mathsf{QMA_1}$. As a consequence, quantum $3$-SAT is $\mathsf{QMA}$-complete. The construction relativizes to classical oracles, so known classical-oracle separations of $\mathsf{QMA}$ from $\mathsf{QCMA}$ extend to $\mathsf{QMA_1}$.

Quantum Physics (quant-ph); Computational Complexity (cs.CC)

arXiv:2609.13032 [quant-ph]

(or arXiv:2609.13032v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.13032 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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