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.
Quantum 3-SAT is QMA1-complete
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abstract
Quantum satisfiability is a constraint satisfaction problem that generalizes classical boolean satisfiability. In the quantum k-SAT problem, each constraint is specified by a k-local projector and is satisfied by any state in its nullspace. Bravyi showed that quantum 2-SAT can be solved efficiently on a classical computer and that quantum k-SAT with k greater than or equal to 4 is QMA1-complete. Quantum 3-SAT was known to be contained in QMA1, but its computational hardness was unknown until now. We prove that quantum 3-SAT is QMA1-hard, and therefore complete for this complexity class.
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quant-ph 1years
2025 1verdicts
CONDITIONAL 1representative citing 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.