Automated system solves Aaronson-Ambainis quantum conjecture in three days
Physics research startup PSI uses Anthropic models and Lean verification to tackle an 18-year-old computing question.
A computational research system has generated a formal mathematical proof for the Aaronson-Ambainis conjecture, an 18-year-old open problem concerning the limits of quantum computing. Physics research firm PSI announced that its automated platform produced the verification within three days, employing artificial intelligence to address when conventional machines can approximate quantum algorithms.
An 18-year-old limit on quantum advantage
First proposed in 2008, the Aaronson-Ambainis conjecture explores the exact boundaries where quantum processors retain an exponential speed benefit over standard digital architectures. According to reporting by Interesting Engineering, the conjecture focuses on whether quantum algorithms that feature a specific mathematical structure can be simulated by classical hardware with only polynomial overhead. When classical machines simulate processes on randomly chosen inputs within polynomial bounds, the apparent operational gap narrows significantly. Established specialized procedures such as Shor's algorithm for factoring integers remain unaffected by the conjecture, as the mathematical question addresses a distinct subset of quantum computations.
Automating formal proof with Lean
To tackle the conjecture, researcher David Turturean led the effort at PSI, developing the automated research workflow, formulating the computational problem, and overseeing execution. The setup ran on PSI's internal infrastructure, using a private, non-public artificial intelligence model developed by Anthropic. During the test run, the platform produced formal statements that were loaded directly into Lean, an interactive proof assistant designed to verify whether logical sequences strictly follow designated mathematical axioms. The system subsequently revised the argument twice, generating a final output that Lean accepted without logical discrepancies.
Independent verification and academic review
Formal code checking ensures internal consistency, but mathematicians must still establish that the translated theorem matches the original 2008 proposition. Physicist Jim Halverson audited the proof structure, while MIT theoretical physicist Phiala Shanahan examined the formalization created within Lean. In parallel, a mathematics research team at Stanford University consisting of Guy Blanc, Jordan Docter, Carmen Strassle and Li-Yang Tan began evaluating the result. The Stanford group, which had already proved a special case of the Aaronson-Ambainis conjecture in August 2026, is drafting a condensed technical paper to explain PSI's findings to the wider scientific community.
Next steps for automated scientific discovery
The project represents a practical demonstration of innovation in machine-assisted mathematics from PSI, a startup launched publicly in September 2026 to build autonomous discovery engines. While Lean provides programmatic validation of the logic, the proof has not yet completed standard peer review across the academic physics community. Future dissemination and review by external theorists will determine whether the proof resolves the Aaronson-Ambainis conjecture in full.
