AI system cracks 2008 quantum computing conjecture in three days, PSI says

Summary

• PSI says its research system produced a full proof of the Aaronson-Ambainis conjecture, open since 2008.
• The Lean 4 proof assistant accepted the proof; the Lean formalization is public on GitHub under Apache 2.0.
• Machine-checked proofs would compress research timelines, but the written paper still requires human review.

The latest

A quantum computing conjecture open since 2008 now has a proof that a computer checked automatically. Physical Superintelligence announced on 6 November 2026 that its internal research system, running copies of an unreleased and unnamed Anthropic model, generated a complete proof of the Aaronson-Ambainis conjecture on the third day of operation. The company said it then assigned related open problems and the system improved the result twice.

Details

• The conjecture: Scott Aaronson and Andris Ambainis asked whether a quantum computer can be exponentially faster on random, unstructured inputs. They proved that if a specific statement about low-degree polynomials holds, the answer is no. That statement is what PSI says its system has now proved.
• The run: According to PSI, the system produced the full proof on day three on PSI infrastructure, and the Lean proof assistant accepted it. The company then set related open problems; the system strengthened the result twice, and Lean accepted the final version as well.
• The formalization: PSI published the Lean 4 formalization on GitHub under an Apache 2.0 license, using Lean 4.33.0 and Mathlib v4.33.0. A recorded audit found no deferred proof obligations and no added axioms, with the four final theorems resting on three standard axioms only.
• Independent checks: PSI said definitions were re-run through the Lean kernel and through lean4lean, a separate type checker. In an isolated run, a comparison tool using the nanoda and Lean kernels accepted the four theorems; on a second machine it accepted a small correct solution and rejected four deliberately wrong ones.
• The limits: PSI stated the paper itself is not machine-checked, and that matching the formal statement to the conjecture as printed still needs human review. A Lean proof establishes only what its formal statement says: a subtle mismatch would leave the proof valid but answering a different question.
• The people: PSI said David Tortorian of its team built and ran the system, chose the problem, steered the model and reviewed the first draft, and is responsible for the paper's correctness. Jim Halverson audited the proof, and Fiala Shanahan commented on the formal statement.
• Prior groundwork: The proof follows a plan laid out by Shachar Lovett and Jiapeng Zhang, replacing an inequality they had assumed with a new proved one. PSI did not describe the system as working from scratch on the overall strategy.
• Outside reaction: Stanford researchers Guy Blanc, Jordan Docter, Carmen Strassle and Li-Yang Tan, who filed a paper on 19 August 2026 on the conjecture's impact for classical simulation of parallel quantum algorithms, are reading the proof and preparing a shorter exposition. In an assessment published by PSI they called it "a huge result".
• Undisclosed: PSI did not release the total run time, the compute cost, or the extent of human steering involved. It also did not name the Anthropic model powering the system.
• Earlier results: On 23 October 2026, PSI published results on five open problems in quantum information theory, each with a paper, a Lean formalization and verification code. The company said its researchers directed and reviewed that AI-assisted work.

Between the lines

The verification architecture is the claim's real weight: a Lean-accepted proof with no added axioms shifts scrutiny away from whether the argument holds and onto whether the formal statement matches the printed conjecture, which PSI itself flags as a human task. The undisclosed run time and steering level leave the autonomy question open.

What's next

Watch the Stanford group's shorter exposition of the proof, and any human review confirming the Lean statement matches the conjecture as originally printed by Aaronson and Ambainis.

Source: Physical Superintelligence (psi.inc), Unite.AI, explainX, Runtime Wire