AI physics startup PSI says a system running a non-public Anthropic model proved the Aaronson-Ambainis conjecture, a quantum computing question open since 2008

Quantum computers will not provide exponential speedups for all problems, limiting their advantage to structured inputs.

Physical Superintelligence (PSI), a startup focused on AI and physics, has announced a proof for the Aaronson-Ambainis conjecture, a fundamental question in quantum computing that has remained open since 2008. The proof was discovered by an internal research system developed at PSI, which utilized a non-public Anthropic language model. This system successfully found and verified the proof on its own infrastructure, with the Lean proof assistant confirming each step. The Aaronson-Ambainis conjecture is crucial as it addresses whether quantum computers can achieve exponential speedups on random inputs, a scenario where they currently lack a known advantage. The conjecture's resolution indicates that for general yes-or-no questions, quantum computers offer at most polynomial speedups on random inputs, not exponential ones, unless the input has a specific rare structure. This finding helps delineate the boundaries of quantum computational advantage.

The successful application of an AI system, running a proprietary Anthropic model, to solve a complex, long-standing mathematical conjecture in quantum computing signifies a major advancement in AI-assisted scientific discovery. It demonstrates the potential for large language models to move beyond text generation into complex reasoning and proof discovery in highly specialized scientific domains. This development could accelerate breakthroughs in fields like physics and mathematics by offloading intensive theoretical work to AI systems, potentially reducing the time and resources required for researchers to tackle fundamental problems.

This event highlights a growing trend of AI models tackling challenging scientific questions, potentially shifting the landscape of theoretical research. It suggests that companies developing advanced AI models, like Anthropic, may find significant new markets in scientific and academic research. The reliance on a non-public model also underscores the ongoing proprietary development in cutting-edge AI, where the most impactful applications might not be immediately accessible or reproducible by the broader research community.