PSI's AI system proves the 18-year-old Aaronson-Ambainis conjecture, Lean-verified in 3 days
anirbanbandyo · x · 2026-11-08
Physical Superintelligence (PSI) announced that its internally built research system, running a non-public Anthropic model on its own infrastructure, found a complete proof of the Aaronson-Ambainis conjecture — a central open problem in quantum complexity theory since 2008.
- The theorem settles when quantum computers can be exponentially faster: on unstructured random inputs, they gain at most polynomial speedup; exponential advantages like Shor's algorithm depend on hidden structure in the input
- The system found the complete proof on day three of the run, with every step machine-checked by the Lean proof assistant; it then improved the result twice while working on related open problems
- The proof builds on ideas from Shachar Lovett & Jiapeng Zhang, David Reimer, and others
More from AGI Musings
- Mech interp is a data problem: 10K labeled tasks could localize reward hacking — burny_tech · 2026-11-08
- Gary Marcus calls out Anthropic CEO's AI job-loss claims: 'numbers out of a hat' — GaryMarcus · 2026-11-08
- Australia moves to restrict screens and AI in schools, drawing criticism it will leave kids behind — CtrlAltDwayne · 2026-11-08
- Valuation Guru Damodaran Dismisses 'AI Will Triple GDP' Hype: 40 Years of Data Show No Productivity Gain — GaryMarcus · 2026-11-08
- AI-Generated Resumes Are Flooding the Job Market, Shifting Hiring From Polish to Proof — mdancho84 · 2026-11-08
- Every's Thesis 2027 recap: livestream chat from 15 countries on AI and agency — danshipper · 2026-11-08