For polynomial-resource black-box procedures, the achievable QMA completeness cannot be closer to one than doubly exponentially, and soundness cannot become super-exponentially small, relative to a quantum oracle.
The selected contribution is GPT-5-Thinking’s original rational-trace strategy for the completeness barrier; the current published proof uses Phillip Harris’s determinant instead.
For polynomial-resource black-box procedures, the achievable QMA completeness cannot be closer to one than doubly exponentially, and soundness cannot become super-exponentially small, relative to a quantum oracle.
The theorem matches the previously known doubly-exponential completeness construction and makes Aaronson's earlier perfect-completeness oracle barrier quantitative.
Can a polynomial-resource black-box QMA amplification procedure exceed the known completeness and soundness thresholds relative to a quantum oracle?
Publication dates and editorial changes.
GPT-5's rational-function step in an early QMA amplification proof
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