Teams of AI agents working in the Lean theorem prover found quantum programs that cut resource costs by more than 290x on one arithmetic subroutine, and by 10.9x, 8.08x and 2.49x on simulations relevant to fusion, photochemistry and drug metabolism, according to a paper posted to arXiv on 6 November by researchers at Google DeepMind and Google Quantum AI. Each program comes with machine-checked proofs of correctness and cost.
By our arithmetic, 39% of the cost reduction in the three simulations came from ideas the agent teams shared with each other: the paper puts 15% on a shared wiki and 24% on scheduled conferences between teams, with 61% from ideas found within a team.
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The key insight: As we read it, the paper moves the human work to the specification: researchers write what a quantum program must compute and may cost, AI agent teams search and prove, and the Lean checker accepts or rejects. By our arithmetic, 39% of the cost reduction in three simulations came from ideas shared across teams.
The paper starts from a constraint: “quantum algorithms can only be evaluated by classical computers on restricted or small instances”. Its answer is to replace testing with proof. Researchers write a problem specification in Lean that states what a program must compute and what it may cost, and leave placeholders for the agents to fill with a program, a cost bound and the proofs.
An external verifier then checks every submission against the frozen specification using the Lean Comparator, confirming that the target theorems, definitions and allowed axioms are unchanged. The paper says researchers therefore review only the specification before a run.
Cost is measured as spacetime cost, the number of qubits times the number of T gates, which the paper describes as costly in error-corrected quantum computers. The authors list 25 names, among them Sergio Boixo, Ryan Babbush and Pushmeet Kohli.
Where each verified cost cut came from in three quantum simulations, once sharing between agent teams was active, as a share of the log cost reduction (paper Fig. 5b). The 39% cross-team total and the 4% stopping-power conference share are our arithmetic.
The Results
For fixed-point arcsin, a subroutine for loading numbers into a wavefunction, the cost fell from more than 1.08 x 10^8 to 3.70 x 10^5, the 290x figure, combining classical and formal search. For stopping power in fusion, cost fell from 5.42 x 10^15 to 4.98 x 10^14 (10.9x).
Non-Born-Oppenheimer dynamics, a photochemistry problem, fell 8.08x, and cytochrome P450 energies, relevant to drug metabolism, fell 2.49x. For parallel Grover search, the verified circuits cut expected rounds by up to 1.22x for finding one item and up to 1.41x for finding all marked items, and matched the baseline on the boundaries.
How the Teams Shared Work
Each researcher configured an independent team of LLM agents, choosing the framework, models, prompts and division of labour. Teams posted verified solutions, reusable Lean files and notes on dead ends to a shared wiki, and met every four hours in a forum the paper calls conferences.
In non-Born-Oppenheimer dynamics, the paper says “the leading record changed teams seven times” after the first run, and the final circuit combines techniques from three of seven participating teams. The largest single drop, 34%, began as a conference proposal from one team that a second team refined and proved.
The cross-team share ranged from 13% in stopping power to 63% in cytochrome P450, according to the paper, which notes that credit is often hard to separate cleanly.
Where the Checks Mattered
The paper says agents may exploit loopholes by weakening theorem statements, altering definitions or adding axioms, which is why the external verifier exists. Flawed candidates fell into two groups: broken proofs or inaccurate estimates, which the verifier and conference critique filtered out, and loopholes in the specifications, such as exploiting how Toffoli gates were counted without improving the circuit, which researchers closed by revising the specification.
The Structural Read
As we read the results, the proof is what let teams build on one another without manual code review, which the paper itself says makes open collaboration safe at this scale.
Shirobokov, Jaderberg et al., arXiv:2611.09822
“quantum algorithms can only be evaluated by classical computers on restricted or small instances”
Three Implications
FOR AGENTIC CODING The paper pairs agent-written programs with machine-checked proofs of correctness and cost, checked against a frozen specification by an external verifier.
FOR RESEARCHERS The paper says formal AI discovery shifts where human effort is applied: researchers choose problems, prepare formal specifications and interpret the verified solutions.
FOR QUANTUM COMPUTING The paper reports cost cuts of 10.9x, 8.08x and 2.49x on fusion, photochemistry and drug-metabolism simulations, and says they still demand far more resources than projected for the first fault-tolerant machines.
The framework names “The Verifier Moat — built by RLVR on domain-specific reward signals, building into a new asset class for reasoning-heavy verticals.”
As we read it, a Lean specification plus an external checker is a verifier of exactly that kind for quantum programs. The framework predates this paper and does not discuss it.
What Is Not Established
This is a preprint posted to arXiv. The paper says each researcher chose the models used; the sections we read do not name them, and we have not seen compute or cost figures for the agent runs. The authors say their Lean library will be open sourced shortly with the specifications and solutions.
The paper also says its end-to-end simulations still demand far more resources than projected for the first fault-tolerant quantum computers, and that agents “cannot optimize beyond” the specifications researchers write.
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Google DeepMind and Google Quantum AI report AI agent teams that found quantum programs more than 290x cheaper on one subroutine and 2.49x to 10.9x cheaper on three science simulations, each with machine-checked proofs. By our arithmetic, 39% of the simulation gains came from ideas shared across teams. As we read it, the human work moved to writing the specification, and the proof checker decides what counts.
A note on sourcing. This report is based on the arXiv preprint 2611.09822 by researchers at Google DeepMind and Google Quantum AI, read on 9 November 2026. It has not been peer reviewed. The 39% cross-team share is our arithmetic from the paper’s Figure 5b; all other figures are the paper’s.
Gennaro Cuofano is a CRO and tech executive who has worked in AI since late 2015, starting with bringing NLP, natural-language generation, voice and chatbot products to the marketing industry. His background is in law and finance: he holds a Master's degree in Law and an International MBA with an emphasis on corporate finance (LUISS Business School and the University of San Diego, 2012), and worked as a financial analyst at a real-estate investment firm in San Diego and as an assistant controller. His work focuses on business model strategy, business engineering and, more broadly, structural analysis: how companies make money, read from their own filings. He created FourWeekMBA and leads research there and at The Business Engineer, his newsletter on AI and business strategy, with over 95,000 subscribers and more than 1,000 published analyses. His writing has also appeared on Entrepreneur (for example, How to Digitize a Family Business in Europe) and HackerNoon. Find him on LinkedIn and Substack. See how we source.
