AI Proof Closes 2008 Quantum Computing Conjecture
The announced proof awaits outside peer review, and a related Stanford result separately narrows where quantum speedups can arise.
Updated on Nov. 6, 2026 in Quantum Computing
Physical Superintelligence said an AI system proved the Aaronson-Ambainis conjecture, a quantum computing question open since 2008. The proof is announced, not yet peer reviewed; outside review is pending, though Lean accepted a complete machine-checked proof on day 3 of the run.
Why it matters
The claim matters because a long-standing theoretical question in quantum computing is reported closed by an AI system rather than by human researchers alone. Stanford researchers separately proved a related no-speedup result, so the field is moving on both fronts at once.
The proof was checked step by step in the Lean proof assistant, which accepted a complete machine-checked version on day 3 of the run. The AI system ran on company infrastructure using instances of a non-public Anthropic model, and its outputs remain unreviewed by external experts.
The players
Physical Superintelligence
An AI company that built the system used to prove the conjecture and published a paper and public Lean formalization of the result.
David Turturean
The researcher who led the work, built the AI system, scoped the problem, and remains responsible for the proof's correctness.
Stanford University
The institution whose researchers Guy Blanc, Jordan Docter, Carmen Strassle, and Li-Yang Tan proved the related no-speedup result for parallel-round quantum algorithms.
The details
The AI system ran on company infrastructure after David Turturean built it and scoped the problem, and he prompted a first paper draft from it. Lean, a proof assistant that checks each logical step mechanically, verified every step of the proof. The Lean sources are posted in a public GitHub repository so others can inspect them.
Timeline
The Aaronson-Ambainis conjecture was first posed as an open question in 2008.
Stanford researchers proved their related no-speedup result in August 2026.
Physical Superintelligence announced the AI proof on November 6, 2026.
The Tech Race
The Aaronson-Ambainis conjecture has been open since 2008, and Physical Superintelligence's AI-produced proof is announced ahead of outside peer review. Stanford researchers' August 2026 proof of a related no-speedup result shows parallel work on the same family of quantum speedup questions.
The result is a theoretical proof and does not produce a product or service available to users. Practical effects would depend on future work, and no availability timeline has been announced.
The takeaway
Watch for outside peer review of the Aaronson-Ambainis proof, which is pending and will determine whether the claim holds up. The Stanford expert exposition of the related no-speedup result is also in progress.
Further reading
Explore more in Quantum Computing to see how theoretical advances like this one connect to the field's broader research.
