Scott Aaronson credits GPT-5 with a key step in a quantum complexity proof
In 'Limits to black-box amplification in QMA' (Aaronson and Witteveen, arXiv 2509.21131), GPT-5-Thinking suggested the key function Tr[(I−E(θ))^−1] used in the proof. Aaronson called it the first paper of his where a key technical step came from AI.
Key facts
- Result: black-box amplification cannot push QMA completeness error below doubly exponential or soundness error below exponential
- Aaronson: 'Within a half hour, it had suggested to look at the function…'
- Aaronson: 'if a student had given it to me, I would've called it clever'
- Blog post 'The QMA Singularity', 27 Sep 2025
Science result
- Field
- computer-science / quantum complexity theory
- Problem
- Limits of black-box error reduction in QMA
- Result
- Proof of tight limits on black-box amplification in QMA, with the central analytic idea proposed by GPT-5.
- AI system
- GPT-5-Thinking
- Human role
- Human-led with AI tools: humans posed the problem, checked and wrote the proof
- Verification
- Expert-checked; arXiv preprint
- Status
- confirmed
- Why surprising
- A leading complexity theorist said an LLM supplied the idea he would have called 'clever' from a student.
What happened
Stuck on a technical step, Aaronson asked GPT-5 for help. Within about half an hour it proposed analysing a resolvent-trace function, which worked.
Why it matters
It was a credible, first-person account from a top theorist of an LLM contributing a genuine idea to a published result.
Changelog
- 2026-09-29: created
Related events
Sources (3)
- discussionScott Aaronson: The QMA Singularity
- paperLimits to black-box amplification in QMA (arXiv 2509.21131)
- pressThe Quantum Insider: GPT-5 serves as research assistant
id: 2025-09-27-aaronson-gpt-5-qma-proof · updated 2026-09-29 · open in the interactive timeline