{"slug": "an-unreleased-anthropic-model-solved-an-18-year-old-quantum-computing-problem-a", "title": "An unreleased Anthropic model solved an 18-year-old quantum computing problem, a startup says", "summary": "Physical Superintelligence (PSI), a public benefit corporation, said on Friday that a research system running \"instances of a non-public Anthropic model\" produced a proof of the Aaronson-Ambainis conjecture, open since 2008, and that the Lean proof assistant accepted it with no placeholder and no added axiom, re-checked by two independent Lean kernel implementations. The proof, which PSI says was complete on the third day of the run and later improved twice, has not been peer reviewed; PSI published the paper and full machine-checked proof on GitHub, with technical staff member David Turturean named as responsible for the paper's correctness and adviser Jim Halverson auditing it. Four Stanford University researchers — Guy Blanc, Jordan Docter, Carmen Strassle and Li-Yang Tan — said \"This is a huge result,\" though a 2019 claimed proof by Nathan Keller and Ohad Klein was withdrawn within weeks after a flaw surfaced.", "body_md": "The Anthropic logo. Image: Anthropic\n\nA physics AI startup says a research system running an unreleased Anthropic model has solved one of the best-known open problems in quantum computing. Physical Superintelligence (PSI) [said on Friday](https://psi.inc/research/aaronson-ambainis/) that the system found a proof of the Aaronson-Ambainis conjecture, a question about how much faster quantum computers can really be, which had been open since 2008, and that a computer proof checker accepted it.\n\nThe proof has not been peer reviewed. PSI has published the [paper and the full machine-checked proof](https://github.com/physical-superintelligence/aaronson-ambainis) on GitHub so that others can check it.\n\n## What PSI says its system did\n\nPSI, a public benefit corporation that calls itself an \"AI-native laboratory\" for physics, says the work came from a system it built in-house and ran on its own infrastructure. It says \"instances of a non-public Anthropic model\" were used in the run, but doesn't name the model.\n\nAccording to the company, the system had a complete proof during the third day of the run, and Lean, a proof assistant in which a computer checks every step of a mathematical argument, accepted it. PSI then set the system loose on related open problems, and says it improved the result twice along the way.\n\nThe GitHub notes are blunt about who did what: the mathematical statements, the first draft of the paper and the Lean formalisation \"were produced by AI models\". David Turturean, a member of PSI's technical staff, built the research system, chose the problem, prompted the model to write up the results, reviewed the draft and is named as responsible for the paper's correctness. PSI adviser Jim Halverson audited the proof.\n\n## Why this problem matters\n\nQuantum computers are known to be dramatically faster than ordinary ones on some problems, such as breaking numbers into their prime factors with Shor's algorithm. But those speedups rely on structure: a hidden pattern in the input that the quantum machine can exploit. The open question was whether a quantum computer could be exponentially faster on random inputs, which almost never have such a pattern.\n\nScott Aaronson and Andris Ambainis turned that into a statement of pure mathematics about low-degree polynomials whose values stay between 0 and 1: such a polynomial, unless it is nearly constant, must have at least one input bit that strongly moves its value. In [their paper](https://arxiv.org/abs/0911.0996), they showed that if the conjecture is true, quantum computers can be at most polynomially faster than ordinary ones on random inputs, never exponentially.\n\nPSI says its proof follows a plan laid out by Shachar Lovett and Jiapeng Zhang, who had left one key inequality unproved. The new paper proves a replacement inequality and gives an explicit bound.\n\n## \"This is a huge result\"\n\nIn August, four Stanford University researchers proved the conjecture's prediction in a special case. PSI says they have since been reading its proof of the full conjecture, have sent comments and are writing a shorter version for experts. PSI quotes them:\n\nThis is a huge result. It resolves a decades-old conjecture with important implications for the nature of problems that admit quantum speedups.\n\nGuy Blanc, Jordan Docter, Carmen Strassle and Li-Yang Tan, Stanford University, as quoted by PSI\n\n## What hasn't been checked yet\n\nThis conjecture has fooled people before. In 2019, Nathan Keller and Ohad Klein posted a claimed proof, which Aaronson [announced on his blog](https://scottaaronson.blog/?p=4414); within weeks a flaw turned up and the paper was withdrawn.\n\nThe Lean proof is what makes PSI's claim harder to dismiss. The repository says the main theorems are proved \"with no placeholder and no added axiom\", and that they were re-checked by two independent implementations of the Lean kernel. What a checker can't confirm is that the formal statement matches the conjecture as Aaronson and Ambainis meant it, so PSI has put that statement in a short file that imports nothing but Lean's maths library, for experts to compare.\n\nNeither Aaronson nor Ambainis had commented publicly by the time of publication. Anthropic hasn't commented on the result or on which model PSI used.\n\nIt lands in a crowded few weeks for AI maths. [Microsoft researchers said AI agents helped crack the 31-year-old KLS conjecture](https://madrobot.blog/2026/10/21/microsoft-kls-conjecture-proof-ai-agents-31-year-old-maths-problem/), and [OpenAI and Anthropic both claimed big results on the same day](https://madrobot.blog/2026/10/27/openai-ai-proofs-kakeya-eth-yang-mills-claude/), which Aaronson greeted on his blog as an \"endless buffet\". Not every claim survives: OpenAI [pulled three of 722 AI-written maths papers](https://madrobot.blog/2026/10/08/openai-722-maths-papers-github-three-withdrawn-mathematicians-react/) a day after posting them. Quantum computing is a growing target too: Claude recently [beat the best published quantum circuits](https://madrobot.blog/2026/10/17/claude-mythos-quantum-circuits-beat-best-published-designs-53-hours/).\n\n## Why it matters\n\nIf it holds up, an AI system has settled a central question about the limits of quantum computing, with a proof a machine has already checked line by line. It also shows that Anthropic's unreleased models are already in outside researchers' hands, doing work at the edge of mathematics.\n\n*Sources: [PSI, A proof of the Aaronson-Ambainis conjecture](https://psi.inc/research/aaronson-ambainis/); [PSI on GitHub, paper and Lean formalisation](https://github.com/physical-superintelligence/aaronson-ambainis); [Aaronson and Ambainis, The Need for Structure in Quantum Speedups](https://arxiv.org/abs/0911.0996); [Shtetl-Optimized, The Aaronson-Ambainis Conjecture (2008-2019)](https://scottaaronson.blog/?p=4414).*", "url": "https://wpnews.pro/news/an-unreleased-anthropic-model-solved-an-18-year-old-quantum-computing-problem-a", "canonical_source": "https://madrobot.blog/2026/11/06/anthropic-model-proves-aaronson-ambainis-quantum-conjecture/", "published_at": "2026-11-06 20:18:00+00:00", "updated_at": "2026-11-06 20:23:59.955758+00:00", "lang": "en", "topics": ["artificial-intelligence", "ai-research", "large-language-models", "ai-safety"], "entities": ["Anthropic", "Physical Superintelligence", "David Turturean", "Jim Halverson", "Scott Aaronson", "Andris Ambainis", "Lean", "Stanford University"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/an-unreleased-anthropic-model-solved-an-18-year-old-quantum-computing-problem-a", "markdown": "https://wpnews.pro/news/an-unreleased-anthropic-model-solved-an-18-year-old-quantum-computing-problem-a.md", "text": "https://wpnews.pro/news/an-unreleased-anthropic-model-solved-an-18-year-old-quantum-computing-problem-a.txt", "jsonld": "https://wpnews.pro/news/an-unreleased-anthropic-model-solved-an-18-year-old-quantum-computing-problem-a.jsonld"}}