# PSI proves Aaronson-Ambainis conjecture using Anthropic’s non-public model

Digest AI · Research · published 2026-11-06T19:35:01Z

Canonical: https://digestai.news/story/psi-proves-aaronson-ambainis-conjecture-using-anthropics-non-public-mo

## Summary

Physical Superintelligence (PSI) announced on November 6 that its internal research system, running a non-public Anthropic model, proved the Aaronson-Ambainis conjecture—a 2008 open question in quantum computing. The conjecture, proposed by Scott Aaronson and Andris Ambainis, addressed whether quantum computers could outperform classical ones on random inputs without hidden structure. PSI’s system generated a proof within three days, verified by Lean, a proof assistant. The result builds on prior work by Shachar Lovett, Jiapeng Zhang, and others, and was audited by PSI’s advisors, Jim Halverson and Phiala Shanahan.

The breakthrough clarifies that quantum speedups require input structure, ruling out exponential gains on arbitrary inputs. PSI’s David Turturean led the effort, while Guy Blanc and colleagues at Stanford had earlier settled a special case. The proof refines bounds on polynomial influence, a key mathematical concept, and leverages results from combinatorics and probabilistic analysis. Quantum computing’s limitations remain, but this resolves one of its most enduring theoretical puzzles.

## Key points

- PSI’s system proved the Aaronson-Ambainis conjecture using Anthropic’s non-public model in three days
- Lean verified the proof, which refines bounds on polynomial influence in quantum computing
- Stanford researchers previously solved a special case but confirmed PSI’s full proof

## Why it matters

The proof settles a 16-year-old conjecture, clarifying quantum computing’s limits and guiding research into structured problems where speedups may still apply.

## Sources

1. [AI physics startup PSI says a system running a non-public Anthropic model proved the Aaronson-Ambainis conjecture, a quantum computing question open since 2008](https://psi.inc/research/aaronson-ambainis) (psi.inc, 2026-11-06)

## Cite

Digest AI, "PSI proves Aaronson-Ambainis conjecture using Anthropic’s non-public model", 6 November 2026, https://digestai.news/story/psi-proves-aaronson-ambainis-conjecture-using-anthropics-non-public-mo

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