AI System Proves Aaronson-Ambainis Conjecture
Physical Superintelligence says its AI produced a machine-checked proof of a quantum computing conjecture that had been open since 2008.
Updated on Nov. 6, 2026 in Quantum Computing
Physical Superintelligence announced that an AI system proved the Aaronson-Ambainis conjecture, a problem open since 2008. Lean accepted a complete machine-checked proof on day 3 of the run, and outside peer review of the proof is still pending.
Why it matters
The announcement shows AI systems producing a proof of a long-standing open question in quantum computing, with every step checked by a formal proof assistant. Independent review will determine how much weight the result carries in the field.
The proof was checked step by step in Lean, and the Lean sources are posted in a public GitHub repository. The system ran on instances of a non-public Anthropic model, and the company says it improved the result twice during the run.
The players
Physical Superintelligence
The company that built the AI system and announced the proof of the conjecture, and that has published a paper and a 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 correctness of the proof.
Jim Halverson
The researcher who audited the proof of the Aaronson-Ambainis conjecture.
Phiala Shanahan
The physicist who commented on the Lean formalization of the proof.
The details
David Turturean led the work and remains responsible for correctness, while Jim Halverson audited the proof and Phiala Shanahan commented on the Lean formalization. The AI system ran on company infrastructure after Turturean built it and scoped the problem, and he prompted a first paper draft from the system.
Timeline
2008: The Aaronson-Ambainis conjecture is first posed as an open question.
August 2026: Stanford researchers prove a related no-speedup result.
November 6, 2026: Physical Superintelligence announces the AI proof of the conjecture.
The Tech Race
The result follows a 2008 open problem in quantum query complexity that remained unresolved for nearly two decades. Stanford researchers Guy Blanc, Jordan Docter, Carmen Strassle, and Li-Yang Tan separately proved that parallel-round quantum algorithms gain no exponential speedup on random inputs.
The result is a research milestone in theoretical computer science rather than a consumer product. Its practical relevance depends on whether independent reviewers accept the proof and whether the methods extend to other open problems.
The takeaway
AI systems are beginning to produce formally verified results on open research problems, but the claim is only as strong as the independent review that follows. Readers should watch for expert assessment of the proof before treating it as settled.
What happens next
Outside peer review of the proof is pending, and Stanford researchers are writing a shorter expert exposition of the proof.
Further reading
For background on the field, see the Quantum Computing section.
