Claude designs quantum circuits that beat published records

Anthropic published the research on October 16: “Designing more efficient quantum circuits with Claude.” The setup was simple on paper — Claude got plain-language specs for eight quantum circuits, the basic routines larger quantum algorithms are built from, covering chemistry, optimization, physics simulation, and number theory. An automated evaluator checked each proposal for correctness and scored it on qubits times gates, the standard proxy for how long a circuit takes to run. Then Claude — specifically Claude Mythos 5 — proposed, got scored, and revised, in a closed loop with no human input between rounds.

The work was led by Andi Gu as part of Anthropic's STEM Fellows Program, with mentorship from Alek Kemeny, a quantum physicist at Anthropic, and collaboration with Susanne Yelin of Harvard and Mikhail Lukin of Harvard and QuEra Computing. The paper is on arXiv: “Discovering state-of-the-art quantum circuits with large language models.” Anthropic's own summary line: “Working largely on its own, Claude found designs that improve on the best published circuits, in some cases by an order of magnitude or more.”

First, elliptic-curve point addition — the core step in quantum algorithms for the discrete-logarithm problem on elliptic curves. Claude spent 53 hours on it with minimal prompting and came back with a completely new approach to modular inversion: the first reversible implementation of the divsteps algorithm with no stored branch history. Claude proved new algebraic identities to justify the decoding rule, checked it in large-scale simulations, and formalized it in Lean. One design in the resulting family uses 12% more qubits than the smallest previous circuit but 17 times fewer gates.

Second, a quantum optimizer called decoded quantum interferometry (DQI) — one of the strongest candidates for a superpolynomial quantum speedup, where Google estimates a classically intractable instance would take about three months on the Frontier supercomputer versus roughly an hour on a future quantum machine. Claude rebuilt DQI's most expensive step, the Reed-Solomon decoder, around Berlekamp-Massey decoding instead of the extended Euclidean algorithm, then ran 403 million sample decodings to measure how much memory the circuit actually needs. Result: it sets aside 19 qubits for rare exceptional cases instead of the 665 a worst-case design would reserve, with about one run in 10,000 failing — within the task's allowed error rate. The decoder's gate count fell 12x versus Google Quantum AI's previous construction.

Anthropic says three recurring ideas showed up across the tasks. Conditional routing instead of conditional arithmetic: where an algorithm does different arithmetic depending on a flag, Claude routed operands through controlled SWAPs into one shared arithmetic block instead of building every branch. Information recovery instead of history stacks: rather than storing records needed to run the circuit backward, the designs reconstruct them from the current state. And failure budgets for rare inputs: measure what the task actually needs, reserve memory for the typical case, accept a measured one-in-10,000 failure rate.

For scale on why this matters: in 2017 researchers estimated a quantum computer would need about 50 trillion Toffoli gates to compute the ground-state energy of FeMoco, the iron-sulfur cluster at the heart of nitrogenase. Eight years of work by many research groups brought that down to about 340 million. Claude's elliptic-curve design came from a single 53-hour run.

This is an Anthropic preprint reporting on its own model — no independent peer review, and no outside lab has rerun the evaluator yet. The circuits exist only as software, validated on classical computers; nothing here ran on actual quantum hardware. And Claude did not stroll to these results: Anthropic says it started conservative, repeatedly double- and triple-checking results that were already solid and preferring known approaches, and had to be explicitly pushed to explore qualitatively different designs in parallel.

Anthropic's forward-looking claim: if AI can speed up circuit design, “useful quantum computing could arrive sooner” than expected — putting problems like designing catalysts and understanding new materials within reach of the first fault-tolerant machines. That's a prediction, not a result. The result is the code: eight checkable circuit designs that beat the published best, in some cases by a lot.