Anthropic’s Claude Designs Quantum Circuits That Beat Published Benchmarks

Anthropic researchers used Claude to generate quantum circuit designs for eight computational primitives. In seven cases the AI found versions that needed fewer Toffoli gates and fewer qubits than the best previously published algorithms, according to a research post published Thursday, Oct. 16, 2026. A companion paper, “Discovering state-of-the-art quantum circuits with large language models,” was posted to arXiv the day before.

The team gave Claude Mythos 5 plain-language specifications for eight circuits—drawn from chemistry, optimization, physics simulation and number theory—plus an automated evaluator that checks correctness and scores Toffoli count times peak qubits. Claude proposed Python designs, received scores and revised with little human input between rounds.

Across seven tasks with published baselines, the discovered circuits cut that cost proxy by factors including about 39× (fixed-point Gaussian), 32× (HHL rotation angle), 12× (Reed–Solomon decoder for decoded quantum interferometry), 9.9× (Coulomb potential), 7.7× (nonabelian lattice-gauge simulation) and 4.1× (Fe₂S₂ select). For Reed–Solomon decoding, Anthropic says the change made the costliest DQI step about 12× cheaper than Google’s prior construction after switching from the extended Euclidean algorithm to Berlekamp–Massey and reconstructing temporary values instead of storing them.

In the eighth task, prime-field modular inversion for elliptic-curve point addition, the search produced a new reversible architecture based on divsteps. Compared with the smallest previous design, one circuit in that family uses 12% more qubits but 17× fewer gates; the paper notes prior designs make different Toffoli–qubit trades, so there is no single baseline gain. One complete benchmark circuit uses about 4.0 million Toffoli gates and 935 qubits. A modular-inversion design emerged after a 53-hour autonomous run; Claude also formalized a proof in Lean for its reversible divsteps implementation.

Andi Gu led the project in Anthropic’s STEM Fellows Program, with mentorship from Alek Kemeny, a quantum physicist at Anthropic, and collaboration from Susanne Yelin at Harvard and Mikhail Lukin at Harvard and QuEra Computing. Anthropic notes earlier human-led redesigns for simulating the FeMoco iron–sulfur cluster cut estimated Toffoli needs from about 50 trillion in 2017 to roughly 340 million.

Claude sometimes showed excessive caution; researchers prompted broader exploration. The post says these designs expand qubit-versus-runtime trade-offs rather than claiming a finished fault-tolerant machine.