Limits to black-box amplification in QMA, with the key step written by GPT-5
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 of the first version was produced by GPT-5 in about half an hour; the published version replaces that step with a simpler one suggested by a human coauthor.
- Model
- GPT-5 Thinking
- Field
- Computer science
- Date
- 2025-09-25
- Human collaborators
- Scott Aaronson, Phillip Harris, 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. That matters, because most "AI proved a theorem" stories are not.
Caveats and known objections
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. The paper was published in Quantum on 2026-10-06 (volume 10, article 2227), which is the basis of the peer-reviewed grade, but the published proof no longer uses GPT-5's step. Its author-contributions paragraph says the first version used the rational function GPT-5 suggested, together with a growth bound for complex rational functions, and that after posting Phillip Harris, since added as an author, proposed replacing it with a simpler determinant. So the refereed version certifies the theorem, and the model's contribution is now part of the paper's history rather than its proof; autonomy stays ai-assisted, describing what happened in the first version.
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History of this entry
- RegradedMoved from author verified to peer reviewed on publication in Quantum, and recorded that the published proof replaces GPT-5's step with a simpler one from Phillip Harris, who joined as an author. source ↗
- AddedEntered the registry graded Peer reviewed and AI-assisted.
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Graded peer reviewed for verification and ai-assisted for autonomy. What these mean.
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-limitsBibTeX
@misc{whataifound-utaustin-2025-limits,
title = {Limits to black-box amplification in QMA, with the key step written by GPT-5},
author = {{whataifound.org}},
year = {2025},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by UT Austin / CWI Amsterdam / University of Bonn. Verification: Peer reviewed. Autonomy: AI-assisted.},
url = {https://whataifound.org/finding/2025-09-25-qma-amplification-limits}
}