Year: 2026
Type: preprint
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 $\mathsf{QMA_1}$.
Source: arXiv (Cornell University)
Authors: Grewal, Sabee, Rudolph, Dorian
Institutions: IBM (United States), Columbia University, Paderborn University
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G1587758330
OpenAlex ID: W7212613233
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