PSI claims formal proof of Aaronson-Ambainis quantum computing conjecture

Physics research firm PSI announced that its automated research system completed a mathematical proof of the 18-year-old Aaronson-Ambainis conjecture in three days, according to Interesting Engineering interestingengineering.comInteresting Engineeringinterestingengineering.comOpen source ↗. The problem, originally formulated in 2008, analyzes the boundary conditions under which quantum systems gain an exponential runtime speed advantage over classical computational architectures. The final formalization was verified by the Lean proof-assistant software, though the work has not yet completed full independent academic peer review.

Verification and algorithm structure

PSI stated that its system executed the computation on proprietary infrastructure using an unreleased model from Anthropic. The generated mathematical proof was submitted to the Lean environment, which confirmed that the derived logic holds within the formal system. According to the company, the internal system refined the mathematical argument twice, with Lean verifying the logical validity of the final formulation.

The Aaronson-Ambainis conjecture addresses how much classical information is necessary to simulate specific quantum algorithms. If valid, the conjecture establishes that classical computers can approximate a broad class of structured quantum routines on random inputs with polynomial overhead. This polynomial bound differentiates computations that scale efficiently from those requiring exponential resources, defining why certain quantum routines cannot sustain an exponential speedup. Specific procedures such as Shor's algorithm for prime factorization remain outside the scope of this restriction.

Research team and academic review

David Turturean led the project at PSI, designing the system architecture, formulating the problem, running the computational process, and verifying the paper's contents interestingengineering.comInteresting Engineeringinterestingengineering.comOpen source ↗. Physicist Jim Halverson audited the mathematical proof, and Phiala Shanahan evaluated the Lean formalization.

Stanford University researchers Guy Blanc, Jordan Docter, Carmen Strassle, and Li-Yang Tan, who proved a special case of the conjecture in August 2026, examined aspects of the result and are preparing an exposition of the proof for the scientific community. While Lean confirms that derivations match formal premises, mathematical review must verify whether the formalized premises match the original 2008 conjecture.