QMA has perfect completeness

We prove $\mathsf{Q}\mathsf{M}\mathsf{A}=\mathsf{Q}\mathsf{M}{\mathsf{A}}_{\mathsf{1}}$, 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 $\mathsf{Q}\mathsf{M}{\mathsf{A}}_{\mathsf{1}}$. As a consequence, quantum $3$-SAT is $\mathsf{Q}\mathsf{M}\mathsf{A}$-complete. The construction relativizes to classical oracles, so known classical-oracle separations of $\mathsf{Q}\mathsf{M}\mathsf{A}$ from $\mathsf{Q}\mathsf{C}\mathsf{M}\mathsf{A}$ extend to $\mathsf{Q}\mathsf{M}{\mathsf{A}}_{\mathsf{1}}$.