---
id: "2025-09-27-aaronson-gpt-5-qma-proof"
url: "https://postcutoff.com/e/2025-09-27-aaronson-gpt-5-qma-proof/"
as_of: "2026-11-13T13:49:00+01:00"
date: "2025-09-27"
date_precision: day
category: science
importance: 3
confidence: high
status: [Result confirmed]
verification: Expert-checked
sources: 3
editor: human editor
human_review: null
version: "2026-10-04"
---

As of: 2026-11-13 13:49 CET.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code), with a human editor. How we work: https://postcutoff.com/about/
Canonical page: https://postcutoff.com/e/2025-09-27-aaronson-gpt-5-qma-proof/

# 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

## 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.

## Your AI and this story

- GPT-6 Astra (training cutoff April 2026): in its training data
- Claude Opus 5.5 (training cutoff June 2026): in its training data
- Gemini 4 Hydrogen (training cutoff March 2026): in its training data
- Grok 4.7 (training cutoff May 2026): in its training data

## Sources

1. [Limits to black-box amplification in QMA (arXiv 2509.21131)](https://arxiv.org/abs/2509.21131) (arxiv.org, paper)
2. [The Quantum Insider: GPT-5 serves as research assistant](https://thequantuminsider.com/2025/09/29/gpt-5-serves-as-research-assistant-in-proving-one-of-quantum-computing-theorys-trickiest-theorems/) (thequantuminsider.com, press)
3. [Scott Aaronson: The QMA Singularity](https://scottaaronson.blog/?p=9183) (scottaaronson.blog, discussion)

## Changes

- 2026-09-29 (filed): Created

## Related

- 2025-11-20: [OpenAI publishes 'Early science acceleration experiments with GPT-5'](https://postcutoff.com/e/2025-11-20-openai-gpt-5-science-acceleration/index.md)
- People: [Scott Aaronson](https://postcutoff.com/person/scott-aaronson/)