AI BriefingPhysical Superintelligence Proves Aaronson-Ambainis Conjecture Using AI Research System
·2026.11.06 09:00
Key point
The proof, verified by Lean, establishes that quantum computers cannot achieve exponential speedups on random inputs without specific structural patterns.
Details
- Physical Superintelligence (PSI) proved the Aaronson-Ambainis conjecture, a 2008 open problem in quantum complexity theory, using an internal research system running a non-public Anthropic model.
- The proof was verified by the Lean proof assistant and demonstrates that quantum computers are at most polynomially faster than classical computers on random inputs, settling the question of exponential speedups without structural patterns.
- The system found a complete proof on the third day of the run and improved the result twice, building on the plan of Shachar Lovett and Jiapeng Zhang and utilizing David Reimer's Butterfly Lemma.
- The core mathematical result shows that for bounded polynomials of low degree, some variable has influence at least (v/d)^7, where v is the variance and d is the degree, with a constant c approximately 0.0025.
- Stanford researchers Guy Blanc, Jordan Docter, Carmen Strassle, and Li-Yang Tan had previously settled a special case in August 2026 and are now writing an exposition of the full proof.
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