PSI Reports Machine-Checked Proof of Aaronson-Ambainis Conjecture
What happened
On November 6, 2026, Physical Superintelligence (PSI) announced that its internal research system, using a non-public Anthropic AI model, generated a machine-checked proof of the Aaronson-Ambainis conjecture, a quantum computing problem unresolved since 2008. The proof was produced during the third day of the system's run on PSI's infrastructure and was verified by the Lean proof assistant. PSI further refined the proof by assigning related problems to the system, resulting in two improvements before the final version was accepted by Lean. The manuscript and its formalization in Lean 4 were then released publicly.
Key details
- The Aaronson-Ambainis conjecture concerns the limits of quantum speedups for unstructured problems.
- PSI's proof was generated and checked using a non-public Anthropic model and the Lean proof assistant.
- The proof was improved twice through additional AI-driven iterations before public release.
- David Turturean led the project, with Jim Halverson auditing the proof and Phiala Shanahan commenting on the formalization.
- The formal proof was accepted by both Lean's kernel and an independent implementation, but human review is still required for parts outside the formalization.
Why it matters
Researchers in quantum computing and theoretical computer science now have a machine-checked proof for a conjecture that has shaped understanding of quantum speedups for nearly two decades. This result provides a new formal tool for analyzing when quantum algorithms can be efficiently simulated by classical algorithms, affecting the assessment of quantum advantage in unstructured problems. The public release of the formal proof allows independent verification, but experts must still confirm the alignment between the formalized statement and the original conjecture, as well as review the non-LE