Unreleased AI Model Solves Decades-Old Quantum Computing Conjecture in Three Days

2026-11-08 companies

San Francisco, Saturday, 7 November 2026.
Physical Superintelligence announced an unreleased Anthropic model proved the 18-year-old Aaronson-Ambainis conjecture in just three days, formally verifying all 648 underlying theorems without human error via the Lean proof assistant.

A Historic Breakthrough in Quantum Computing

On November 6, 2026, Physical Superintelligence (PSI), a venture-backed public benefit corporation specializing in quantum research, announced a groundbreaking achievement: an unreleased Anthropic AI model successfully proved the Aaronson-Ambainis conjecture, a long-standing problem in quantum computing theory that had remained unresolved since its formulation in 2008.[1][2][3][6][8][10] The conjecture, which explores the limits of quantum speedups on random inputs, was resolved in a mere 72 hours, marking one of the most significant milestones in automated theorem proving and AI-assisted scientific discovery. The proof was formally verified using the Lean proof assistant, with no placeholders or added axioms, encompassing 648 machine-checked theorems distributed across 84 modules and 761 declarations.[1][2][3][6][8][10]

The Aaronson-Ambainis Conjecture: A Quantum Computing Enigma

Introduced by computer scientists Scott Aaronson and Andris Ambainis in 2008, the Aaronson-Ambainis conjecture addresses whether quantum computers can achieve exponential speedups over classical computers when answering yes-or-no questions on randomly generated inputs.[1][2][3][4][5][8][9] The conjecture posits that such speedups are only possible if the problem exhibits rare structural patterns, effectively limiting the scope of quantum advantages in practical scenarios. Aaronson himself noted that the problem had resisted his efforts for years, stating, ‘I never managed to solve this problem.’[1][3][8] The conjecture is deeply rooted in the analysis of boolean functions and probabilistic combinatorics, drawing connections to earlier work such as Peter Shor’s 1994 quantum factoring algorithm and frameworks by Shachar Lovett and Jiapeng Zhang.[2][5][7][10]

The Role of AI in Scientific Discovery

PSI’s achievement underscores the transformative potential of frontier AI models in accelerating deep-tech research and high-level mathematics. The unreleased Anthropic model, integrated into PSI’s internal research system, autonomously scoped the problem, proposed mathematical pathways, and assembled a complete proof within three days.[1][2][3][6][8][10] The system’s output was then rigorously audited by external advisors, including Jim Halverson and Phiala Shanahan, who verified the Lean formalization and mathematical correctness.[2][10] David Turturean, a Member of Technical Staff at PSI, led the project, prompting the model, refining the draft, and ensuring the proof’s accuracy. The AI’s role extended beyond mere calculation; it synthesized insights from disparate areas of quantum computing theory, including the Butterfly Lemma by David Reimer and contributions from researchers like Avantika Agarwal and Shalev Ben-David.[2][10]

Verification and Implications for Quantum Computing

The proof’s validity hinges on its formal verification via the Lean proof assistant, which checked 648 theorems without human error or added axioms.[1][2][3][6][8][10] The formalized theorem establishes that quantum computers cannot achieve exponential speedups on random inputs without structured patterns, effectively constraining the types of problems that can benefit from quantum advantage.[4][5][7][10] While the conjecture’s resolution is narrow—focusing on input reads rather than total computing time—it carries profound implications for quantum algorithm design and the theoretical limits of quantum computing.[4][5][7][10] Stanford University researchers Guy Blanc, Jordan Docter, Carmen Strassle, and Li-Yang Tan, who had previously settled a special case of the conjecture in August 2026, hailed the result as ‘a huge result’ with ‘important implications for the nature of problems that admit quantum speedups.’[1][2][3][5][6][8][10]

A New Era for AI and Scientific Research

The PSI team’s work represents a paradigm shift in how complex mathematical and scientific problems may be approached in the future. By leveraging an unreleased Anthropic model, the team demonstrated that AI systems can not only assist but autonomously solve long-standing conjectures in quantum computing, a field traditionally dominated by human expertise.[1][2][3][6][8][10] The proof’s publication on GitHub, alongside the formal verification, sets a new standard for transparency and reproducibility in AI-assisted mathematics.[1][2][3][6][8][10] However, the model itself remains private, and the peer-review process for the paper is yet to be completed, leaving some questions about the broader applicability of the approach unanswered.[1][2][3][6][8][10] As the Stanford team prepares a shorter exposition for experts, the quantum computing community watches closely, anticipating further advancements that could redefine the boundaries of automated scientific reasoning.[1][2][5][8][10]

Sources

Artificial Intelligence Quantum Computing