PSI says an internal system proved the Aaronson–Ambainis conjecture

Physical Superintelligence, or PSI, said on 6 November 2026 that an internal research system running a non-public Anthropic model proved the Aaronson–Ambainis conjecture, a question open since 2008 about when quantum computers can be exponentially faster than ordinary ones. PSI said Lean accepted a complete proof on the third day of the run and later accepted two improvements. [1]

What is the Aaronson–Ambainis conjecture?

PSI said on 6 November 2026 that its internal research system proved the Aaronson–Ambainis conjecture. [1] Scott Aaronson and Andris Ambainis asked whether a quantum computer can be exponentially faster on random inputs, which almost never have the hidden repeating structure used by famous speedups such as Shor’s algorithm.

They stated a conjecture about polynomials and showed that, if it is true, quantum computers are at most polynomially faster on random inputs. [1] PSI writes that researchers have counted the conjecture among the central open problems of quantum complexity theory.

How does PSI say the proof was found?

PSI said the system, running a non-public Anthropic model, had a Lean-accepted proof on the third day of the run. [1] The company says the run happened on its own infrastructure, that Lean checked every step, and that the system later improved the result twice, with Lean accepting the final version.

David Turturean, a member of technical staff at PSI, led the work: he developed the research system, scoped the problem, ran it, and prompted the model to package results into a first draft of the paper. [1] PSI also posted proofs and code in a public GitHub repository. [2]

PSI says those Stanford researchers had already proved a special case of the conjecture’s prediction in August 2026, for quantum algorithms that look at their input in a fixed number of parallel rounds. [1] The company says they have been reading the full proof, sent comments, and are writing a shorter exposition for experts.

What would the result mean if the statements match?

If the formal theorem is the original conjecture, PSI says an ordinary computer can predict a quantum computer’s yes-or-no probability, up to a small error, for all but a small fraction of strings, using a number of looks that grows at most like a fixed power of the quantum look-count rather than exponentially. [1]

Readers still need to confirm that the formal Lean statement matches the original 2008 conjecture. [1][2] PSI’s note presents the Lean development as having no placeholders or added axioms and says it was re-checked by independent kernels; this article does not repeat that verification.

Our read

Opinion: A Lean-checked proof of a named 2008 conjecture would be a serious scientific claim, and the Stanford comment PSI quotes is striking—but the claim should be read as “a formal proof exists and experts are checking it,” not as a settled rewrite of quantum complexity until the statements are matched in public.

What we could not verify

• That the Lean theorem is formally identical to the original Aaronson–Ambainis conjecture.
• An independent write-up that is not quoted or hosted by PSI.
• The identity and version of the non-public Anthropic model used in the run.