Physical Superintelligence AI proves Aaronson-Ambainis conjecture

The Aaronson-Ambainis conjecture dates to 2008, when computer scientists Scott Aaronson and Andris Ambainis proposed it as a way to clarify whether quantum computers require hidden regularity to deliver exponential speedups. The question matters because quantum algorithms such as Shor's algorithm, proposed by Peter Shor in 1994 for fast integer factorization, rely on periodic patterns in the numbers being processed. If the conjecture is true, it would mean that for most random inputs, a quantum computer cannot finish a computation with exponentially fewer data accesses than a classical computer — in other words, extreme quantum speedups would need special structure in the problem.

PSI tackled the problem with its own AI research system, which incorporates an undisclosed AI model developed by Anthropic. According to PSI, the system found a complete proof on the third day after execution began, and PSI researchers then refined the proof twice while studying related mathematical questions. Because AI-generated proofs can contain plausible-sounding errors, PSI used the Lean 4 theorem prover to convert the proof into a computer-checkable form. PSI's published materials state that the Lean proof was completed without unfinished parts or new axioms and was confirmed by two independent verification programs, with the paper, Lean source code, verification steps, and logs released on GitHub.

Reactions from experts have been positive but measured. Henry Yuen, a researcher specializing in quantum computing, called it a beautiful question in quantum complexity theory that has now been solved. Mathematician Paata Ivanisvili said it would be a major result if it holds, noting that a positive resolution would essentially mean quantum algorithms can be classically simulated in polynomial time on most inputs for a large class of problems. PSI also says Stanford University researchers who solved a special case of the conjecture in August 2026 have confirmed the proof and are preparing a concise explanation for experts. PSI summed up the result by saying that while many mysteries remain in quantum computing, one mystery has now been reduced.