An AI system running an Anthropic model settled an almost 20-year-old conjecture with implications for “Quantum Speedup”
By Google News AI ·
A US startup called PSI (Physical Superintelligence), not to be confused with the Paul Scherrer Institute, says its AI system, running an unreleased Anthropic model, has proved the Aaronson-Ambainis conjecture, a problem in quantum computing theory that has been open since 2008.
Using Lean, software or an ITP that verifies mathematical arguments, the team checked the proof step by step. In plain terms, when a quantum computer answers a yes-or-no question about random data with no hidden pattern, an ordinary computer can predict its answer for almost every input without needing exponentially more reads of the data.
That matters because the big commercial promise of quantum computing rests on exponential speedups, where the gap over ordinary machines keeps widening as problems grow, and the theorem shows that, at least for yes-or-no questions measured in reads of the data, those only turn up when the data has a pattern to exploit, as in Shor’s factoring algorithm.
Anyone promising exponential gains on messy, unstructured data now has to say where the pattern is. The paper has not been peer-reviewed yet, and neither Aaronson nor Ambainis had commented as of 7 November.
On 6 November 2026, a US startup called Physical Superintelligence, which goes by PSI and describes itself as an AI-native physics laboratory, published a short research note announcing that it had proved the Aaronson-Ambainis conjecture.
The conjecture is a precise mathematical guess that the computer scientists Scott Aaronson and Andris Ambainis wrote down around 2008, and for eighteen years it sat among the central open problems of quantum complexity theory, the branch of computer science that sorts problems by how much effort quantum and ordinary computers need to solve them.
PSI says an internal research system running instances of a non-public Anthropic model produced a complete proof on the third day of a run on the company’s own computing infrastructure, and that Lean, a proof assistant that checks every logical step of an argument, accepted it.
The system was then given related open problems and improved its own result twice; Lean accepted the final version too, and PSI has published the paper and the full formal proof on GitHub.
Aaronson has been making a version of this argument public for twenty years, and his blog’s banner still tells visitors that quantum computers won’t solve hard problems instantly by trying all solutions in parallel. The new theorem puts a proof behind part of that warning, at least for yes-or-no questions on random data.
A quantum speedup is the saving a quantum computer offers over the best ordinary computer on the same problem. Complexity theorists measure it by how the work grows as the problem gets bigger, because a quantum machine that needs a thousand steps where an ordinary one needs a million is only worth having if the gap holds up as the input doubles, and doubles again.
A polynomial speedup, where the quantum machine’s effort is a fixed power of the ordinary machine’s, is modest. Lov Grover’s 1996 search algorithm is the standard example: it finds a marked item in an unsorted list of N entries in roughly the square root of N steps, so a million entries take fewer than a thousand steps (Grover’s paper).
An exponential speedup is the big prize, because the ordinary computer’s effort roughly doubles every time the input grows by a fixed amount while the quantum computer’s climbs far more slowly, and the best-known example is…
Originally published by Google News AI
