Artificial intelligence has helped prove a long-standing mathematical conjecture that establishes a fundamental limit on the advantages quantum computers can offer when solving certain problems involving large amounts of random data.
The proof, produced using Anthropic’s Fable 5.2 AI model by researchers at the start-up Physical Superintelligence (PSI), resolves a question that mathematicians and computer scientists had been unable to settle for decades. It confirms that, for a particular class of mathematical problems, conventional computers can approximate the performance of quantum computers without requiring substantially more computational effort.
The result establishes that quantum computers do not necessarily have an advantage when processing problems with little mathematical structure and highly random inputs. It also removes an entire category of problems from the search for tasks in which quantum computing could deliver significant performance gains.
The question originated in 1999, when Scott Aaronson of the University of Texas at Austin began examining the circumstances under which quantum computers could outperform conventional computers. Researchers already knew of examples of quantum computational advantages, most notably Shor’s algorithm for factoring numbers. However, Aaronson suspected that such advantages depended on particular mathematical structures underlying the problems being solved.
He subsequently considered whether quantum computers could also demonstrate superior performance when confronted with problems dominated by randomness rather than mathematical structure. In 2011, Aaronson and Andris Ambainis of the University of Latvia formally proposed the Aaronson-Ambainis (AA) conjecture, suggesting that, in at least one such case, quantum computers would not have a significant advantage. They were unable to establish a proof.
The conjecture concerns a computer’s ability to answer a yes-or-no question after receiving a very large random string of binary digits, consisting of ones and zeroes. The central question is whether a quantum computer could obtain the answer by examining the string significantly fewer times than a conventional computer. The conjecture proposed that, for most such strings, a conventional computer could approximate the quantum computer’s performance without taking substantially longer.
Aaronson and Ambainis translated the central statement into the mathematical language of polynomials, turning the problem into a question within another area of pure mathematics. That approach attracted researchers beyond quantum computing. “We didn’t think it would catch on like it did. People who were powerhouses in their own fields and didn’t care about quantum computing got interested,” Aaronson said.
David Turturean of PSI and his colleagues used Anthropic’s Fable 5.2 to produce the proof. According to Turturean, the AI model, which was not publicly available at the time, completed the initial proof, refined it twice and verified the final version using Lean, a mathematical proof-checking software system, in approximately four days.
The researchers subsequently shared their work with Guy Blanc, Jordan Docter, Carmen Strassle and Li-Yang Tan at Stanford University in California. The four mathematicians examined the proof and prepared an exposition explaining its principal components.
In a joint statement to New Scientist, the Stanford researchers said the new proof substantially advanced the mathematical work on which it was based. “The proofs are entirely different – and substantially more difficult. Everything is also woven together in a novel way,” they wrote.
Shachar Lovett of the University of California, San Diego, whose research contributed to the proof, said the Stanford team’s explanation identified mathematical techniques that other researchers could learn from and reuse. He said AI tools could help mathematicians pursue more ambitious research questions.
However, the researchers cautioned against interpreting the result as a major practical setback for quantum computing. Lovett described the work as primarily mathematical, while Aaronson said it ruled out a potential direction for finding quantum speed advantages, although he had not considered it a particularly promising one.
The Stanford researchers said the result did not eliminate the possibility of quantum advantages in other areas. Problems involving shorter or less random input strings, or those requiring answers beyond a simple yes or no, could still favour quantum computers. Potential applications include simulating industrially relevant molecules and solving certain optimisation problems.
Ambainis said the next challenge would involve identifying new mathematical questions. “There is some major creative leap needed. I think that’s something where AI is not good yet,” he said.
