Startup says an unreleased Anthropic AI model proved an 18-year-old quantum computing conjecture
A computer proof checker accepted the result, Physical Superintelligence says. Stanford researchers are reading it, but it has not been peer reviewed.
Physical Superintelligence, a research startup known as PSI, said Nov. 6 that its in-house research system, running a non-public AI model from Anthropic, proved the Aaronson-Ambainis conjecture, a math problem open since 2008. A conjecture is a statement experts suspect is true but no one has proved.
What the problem asks
Quantum computers use the odd rules of tiny particles to calculate, and for some problems they are expected to be vastly faster than ordinary computers. The best-known example, Peter Shor's 1994 method for breaking big numbers into factors, works because the input hides a repeating pattern, PSI explains. Scott Aaronson and Andris Ambainis showed that if their conjecture is true, quantum computers can be only modestly faster, not vastly faster, on random inputs with no such pattern. PSI says the proof settles that question.
How it was checked
PSI says its system had a full proof on the third day of the run, and Lean, a program that checks every step of a math proof, accepted it. The system later improved the result twice, PSI says. The company does not name the Anthropic model or say how much computing the run used, and staff member David Turturean is responsible for the paper's correctness.
Four Stanford University researchers, Guy Blanc, Jordan Docter, Carmen Strassle and Li-Yang Tan, proved a special case in August. PSI says they are reading the full proof, have sent comments and called it a huge result in a note PSI published.
Why caution is warranted
Big proofs can fall apart. In 2019, two other researchers withdrew a claimed proof of this same conjecture after what looked like a fatal flaw turned up, Aaronson wrote on his blog. PSI's proof has not been published in a peer-reviewed journal. PSI says it has raised more than $58 million in a round led by Breakthrough Energy Ventures.
Source: PSI announcement; PSI proof files; PSI home page; Scott Aaronson's 2019 post