A significant conjecture in quantum computing has been resolved in three days, ending 18 years of uncertainty.

A mathematical problem concerning the limits of quantum computing, after 18 years of research, may have been solved in just three days. The physics research company PSI claims to have cracked the long-standing Aaronson-Ambainis conjecture, a breakthrough that could provide new insights into when quantum computers might surpass traditional computers. The company stated that its system completed a proof of the Aaronson-Ambainis conjecture within three days. This problem was first proposed in 2008 and involves the conditions under which quantum computers can achieve exponential speed advantages compared to classical computers.

Research System that Solved the Conjecture

PSI stated that its research system utilized a proprietary model from Anthropic, running on the company's own infrastructure. The system generated a mathematical proof, which was accepted by the formal proof assistant software Lean for checking logical correctness. The company noted that the system subsequently made two improvements to the proof, and the final version was also accepted by Lean. However, the results have not yet undergone comprehensive independent academic review.

Researchers at Stanford University have reviewed certain aspects of the work and provided feedback, but broader review will be crucial in determining whether the proof resolves the original conjecture. The Aaronson-Ambainis conjecture addresses a long-standing quantum issue, explaining how much information classical computers need to simulate certain quantum algorithms. More specifically, it focuses on whether quantum algorithms with specific mathematical structures can be effectively approximated by classical computers. If the conjecture holds, classical computers would require only polynomially more computation to simulate on randomly chosen inputs.

Advantages and Limitations of Quantum Computing

This distinction is significant, as polynomial growth and exponential growth lead to vastly different computational demands as problem sizes increase. This helps explain why some quantum algorithms may not deliver exponential advantages over classical computing, even if quantum hardware can process information in fundamentally different ways.

This result does not imply that quantum computers have no advantages over classical machines. Algorithms designed for specific problems, including Shor's algorithm for large number factorization, are not excluded by this conjecture. Instead, the conjecture targets a specific class of quantum computing and explores under what conditions their apparent advantages can be reproduced classically. PSI indicated that David Turturean led this work, developing the research system, defining the problem, and overseeing the entire process. He also reviewed the final draft and was responsible for the correctness of the paper.

The company stated that Jim Halverson reviewed the proof, and Phiala Shanahan provided input on its Lean formalization. Stanford researchers, including Guy Blanc, Jordan Docter, Carmen Strassle, and Li-Yang Tan, are also reviewing the results. This group previously proved a special case of the conjecture in August 2026 and is preparing a summary of PSI's complete proof for other experts.

Their involvement is significant as formal verification and independent mathematical review serve different purposes. Lean can check whether a formal proof logically follows from its stated assumptions, but researchers must also assess whether the formalized statement accurately captures the original conjecture.

PSI was officially launched in September 2026, describing itself as a physics research company focused on building automated systems to facilitate scientific discovery. Its announcement marks a potentially significant milestone, but the statement requires broader expert review to be considered a definitive result.

Significance and Challenges of Solving the Conjecture

PSI's achievement marks an important advancement in the field of quantum computing, particularly in understanding the computational capabilities of quantum algorithms. However, the result still requires extensive academic review to determine its validity and reliability. The potential of quantum computing lies in its ability to solve certain problems much faster than classical computers, but this conjecture resolution serves as a reminder that not all quantum algorithms can provide advantages in every scenario. Future research will need to further explore the specific applications and limitations of these algorithms to fully unlock the potential of quantum computing.