Anthropic: Claude redesigned eight quantum circuits on its own, cutting gates up to 17x and beating Google's decoder design by 12x

Start with method and scope. Anthropic's research page says Claude was given plain-language specifications for eight quantum circuits drawn from chemistry, optimization, physics simulation and number theory, along with an automated evaluator that checks and scores each design. The score is blunt: qubits used multiplied by gate count, a proxy for runtime. Claude Mythos 5 proposed designs in a closed loop, took the feedback and revised, with no human in between rounds. That evaluator works because this class of quantum algorithm has one definite output per input that an ordinary computer can check, and because circuits can be written as code, which plays to the model's strengths. The paper runs 46 pages, was submitted to arXiv on October 15, 2026 (2610.22367), and is by Andi Gu, Alek H. Kemeny, Susanne F. Yelin and Mikhail D. Lukin.

The first concrete result is modular inversion, the costliest step in elliptic-curve arithmetic. The classical divsteps method works well on ordinary computers but never produced a practical quantum circuit because of reversibility: each iteration's choice of operation generates branch information that a classical program can simply discard, while a quantum circuit must retain it to run backwards, which costs a large number of extra qubits. The model's answer was not to store it at all, but to infer — decode — the branch information from the pair of numbers after each iteration, letting the numbers themselves carry the record. That removes the qubit cost of the history.

The second result targets the decoder in the quantum optimization algorithm DQI. DQI works by preparing a quantum state in which good solutions are more likely to be read out, and its most expensive step is an error-correcting decoder recovering a short list of errors from a compact summary; the best prior quantum circuit used the extended Euclidean algorithm. The model judged that algorithm a poor fit — an ordinary program can take a different path per input, but a quantum circuit handling many inputs at once must use one fixed sequence of gates, so the old design was stretched over far more rounds than any single input needed and had to run every operation in every round. The model rebuilt the circuit around Berlekamp–Massey decoding, which performs the same kind of step each round for a fixed number of rounds and therefore suits a fixed gate sequence.

The numbers are all in the original, so do not drop them. In the modular-inversion family, one design uses 12% more qubits than the smallest prior design but 17x fewer gates; overall the family pushes out the Pareto frontier of qubits times runtime. On the DQI decoder, the saving comes from three layers: a different method (extended Euclidean replaced by Berlekamp–Massey), a different architecture (reconstructing temporary values instead of storing them), and a different resource budget (measuring how much memory and computation is really needed). That last layer is the clearest: reserving for the worst case, where an exceptional value arises in 35 different rounds, would take 665 qubits. The model wrote a high-speed simulator and ran 403 million sample decodings, found that almost every run needs to save one value at most, and so set aside 19 qubits, with about one run in 10,000 needing more and failing — inside the task's allowed error rate. Together these cut decoder gates by 12x relative to Google's prior construction.

One piece of background explains why these numbers matter. Anthropic cites FeMoco, the iron-sulfur cluster at the heart of nitrogenase: in 2017 researchers estimated about 50 trillion Toffoli gates to compute its ground-state energy; through a series of algorithmic advances that estimate fell to roughly 340 million gates, a 150,000-fold reduction corresponding to a few hours on a future machine with about three million physical qubits. Those reductions came mainly from redesigning circuits rather than better hardware, which is exactly why circuit optimization pays. Separately, the point-addition exploration ran for 53 hours, with human input limited to the initial brief and occasional prompts to think more broadly.

The boundaries need to be explicit, or this reads as quantum computing arriving early. First, this is vendor-published research and the paper is an arXiv preprint submitted October 15, 2026, with no peer review on record; the evaluator was written by Anthropic, and although it scores programmatically and reproducibly, that is not an independent third-party benchmark. Second, the scope is eight computational primitives, the class of quantum algorithms that can be checked efficiently — the authors say so themselves. Third, every result is at the simulator and gate-count level; nothing ran on real quantum hardware, so the figures are resource estimates, not measured runtimes. Fourth, the baseline is the best previously published circuit, so the size of each improvement depends on that choice, and the 12%-more-qubits-for-17x-fewer-gates point is a trade-off on the Pareto frontier rather than a clean sweep. Fifth, the roughly one-in-10,000 failure rate sits inside the task's allowance but comes from statistical sampling and would need revalidation for a different task.