A quantum oracle separating QMA(2) from QMA
A quantum oracle is constructed relative to which QMA(2) differs from QMA, resolving Watrous's no-disentanglers conjecture, from a proof idea the authors state was generated by a language model.
- Model
- ChatGPT 5.6 Sol
- Field
- Computer science
- Date
- 2026-09-02
- Human collaborators
- John Bostanci, Sabee Grewal, Jonas Haferkamp, Andrew Huang, Yeongwoo Hwang, Anand Natarajan, Chinmay Nirkhe
- Problem posed
- 2009 · open 17 yrs
Sources
Original work
Independent commentary
What was found
The paper exhibits a quantum oracle relative to which QMA is not equal to QMA(2), and derives the no-disentanglers conjecture of Watrous: for every choice of error parameters summing to less than one, any disentangler requires input size exponential in the number of output qubits. The proof combines the unitarily invariant polynomial method of She and Yuen with a construction based on the symmetric and antisymmetric subspace projectors, reducing the QMA lower bound to the approximate degree of OR. The paper carries a section headed 'Tool and computational resource disclosure' which argues that AI-assisted research should record how findings were obtained, and then discloses the model's role.
Novelty check
Whether QMA(2) collapses to QMA has been tracked since Watrous posed the no-disentanglers conjecture, reported by Aaronson, Beigi, Drucker, Fefferman and Shor in 2009. The paper cites the prior partial results it improves on: Harrow, Natarajan and Wu obtained a quasipolynomial lower bound when the error is exponentially small, and Akibue, Kato and Tani proved an exponential lower bound for the more restrictive strong disentanglers. No prior oracle separation was found. The result is new, and is an oracle separation rather than an unrelativized one.
Caveats and known objections
An unrefereed preprint days old at entry, with no formalization and no independent check. The separation is relative to a quantum oracle and does not settle whether QMA(2) equals QMA in the unrelativized world. Autonomy is graded ai-assisted rather than ai-led on the strictest defensible reading of the paper's own account: the authors state that 'the proof idea underlying the main theorem was generated using ChatGPT 5.6 Sol', but also that their initial prompts directed the model to the work of She and Yuen and that they 'subsequently verified, simplified, and developed the argument presented here, and take full responsibility for its correctness'. Humans chose the problem, supplied the key reference and did the development. No transcript has been released, so the phrase 'minimal additional guidance' cannot be checked.
Also recorded at
vibematheda-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma
Nothing mechanically. It is a parallel listing of the same result, carrying its own verification label rather than an independent check.
Nobody outside the lab has checked this yet.
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Entry history (1 event)
- AddedEntered the registry graded Author verified and AI-assisted.
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Graded author verified for verification and ai-assisted for autonomy. What these mean.
Cite this entry
whataifound.org. (2026). A quantum oracle separating QMA(2) from QMA. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-09-02-qma2-oracle-separationBibTeX
@misc{whataifound-mit-2026-separation,
title = {A quantum oracle separating QMA(2) from QMA},
author = {{whataifound.org}},
year = {2026},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by MIT / Columbia / University of Washington. Verification: Author verified. Autonomy: AI-assisted.},
url = {https://whataifound.org/finding/2026-09-02-qma2-oracle-separation}
}