Limits to black-box amplification in QMA, with the key step written by GPT-5
Limits to black-box amplification in QMA, with the key step written by GPT-5 is graded author verified on whataifound.org, with the AI's role graded ai-assisted.
A quantum complexity paper proving black-box error amplification for QMA cannot push completeness closer to certainty than doubly exponentially, in which the pivotal technical step was produced by GPT-5 in about half an hour.
- Verification
- Author verified
- Autonomy
- AI-assisted
- Lab
- UT Austin / CWI Amsterdam
- Model
- GPT-5 Thinking
- Field
- Computer science
- Date
- 2025-09-25
- Human collaborators
- Scott Aaronson, Freek Witteveen
What was found
The authors were stuck on how the largest eigenvalue of a matrix behaved as a parameter varied. GPT-5 proposed reformulating the quantity so that a complex approximation-theory bound applied, and that reformulation became the technical core of the oracle separation. Aaronson wrote that the step would have cost him or a graduate student a couple of weeks and that it was the first substantive AI contribution to a paper of his. The result makes his 2008 oracle separation quantitative and shows recent amplification results are optimal for black-box procedures.
Novelty check
The theorem extends Aaronson's 2008 QMA oracle separation and a 2025 result of Jeffery and Witteveen; no prior bound of this form on black-box amplification appears in the literature. The AI contribution is documented in the paper's acknowledgements and on Aaronson's own blog, not inferred from press coverage — which matters, because most "AI proved a theorem" stories are not.
Caveats
An arXiv preprint. The contribution is one lemma inside a human-conceived and human-written paper; Aaronson is explicit that the model did not pose the problem or design the argument and that he could have done the step himself given time. Autonomy is ai-assisted, which stays the right grade even though the step was pivotal.
Sources
How this is graded
whataifound.org grades every entry on two axes: verification (how solid the result is, from a machine-checked proof down to refuted) and autonomy (how much the AI did versus its human collaborators). This finding is author verified and ai-assisted. Full definitions are in the methodology.
Cite this entry
whataifound.org (2025). Limits to black-box amplification in QMA, with the key step written by GPT-5. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2025-09-25-qma-amplification-limits