One decoder step uses 12 times fewer gates

On 16 October Anthropic described giving Claude plain-language specifications for eight quantum circuits, plus a program that checks and scores each design. Claude Mythos 5 could work in a closed loop: propose a circuit, read the score, and revise, with no person between rounds. Across eight primitives in chemistry, optimization, quantum simulation, number theory, and numerical computing, the authors say it found designs that use fewer qubits and fewer gates than the best published algorithms, in some cases by an order of magnitude or more. That phrase is the summary. The two worked examples below are the specific multiples.

The score is the number of qubits times the number of gates, a proxy for how long the circuit would take. A quantum circuit cannot branch the way an ordinary program does, because it handles many inputs at once. It also cannot throw away scratch work; the only way to discard information is to run the computation that created it in reverse. Saving gates and saving qubits therefore pull against each other.

The first task was elliptic-curve point addition, whose cost is dominated by modular inversion. Claude worked for 53 hours. Human input was limited to the initial brief and occasional prompts to think more broadly. It produced a family of new designs, not a trim of an old circuit. Compared with the smallest previous design, one circuit in the family uses 12% more qubits and 17 times fewer gates. The cited previous designs are Schrottenloher (2026) and Luo et al. (2026). The 17-fold figure is not a single score for all eight tasks, and that particular design uses more qubits, not fewer.

The second task is the expensive Reed–Solomon decoding step inside decoded quantum interferometry. Relative to Google’s previous construction, Claude’s circuit uses 12 times fewer gates. Reserving space for an exceptional value in all 35 rounds would take 665 qubits. After 403 million sample decodings, almost every run needed to save one value at most, so the circuit keeps room for 19 qubits. About one run in 10,000 needs more and fails, which the authors say is within the error rate the task allows. An estimate from Google Quantum AI says one particular optimal-polynomial-intersection problem would take about three months on Frontier and about an hour on a future quantum computer running the algorithm, with most of that hour spent on this decoding. That is an estimate for a future machine, not a clock measured on a machine that exists.

The iron–sulfur cluster FeMoco is background, not this result. A 2017 estimate put the ground-state-energy computation at about 50 trillion Toffoli gates. Later algorithmic work brought the estimate to about 340 million, a roughly 150,000-fold reduction, corresponding to a few hours on a future machine with about three million physical qubits. Anthropic sets those eight years of work beside one 53-hour elliptic-curve run. The 150,000-fold drop does not belong to this experiment.

The authors also record limits. In early experiments Claude was conservative. It second-guessed improvements that were already supported, and it preferred known methods to new ones. They required it to develop several different approaches in parallel, and they sometimes prompted a broader search. The reversible modular inversion came after that push. Once the idea was there, Claude implemented it and checked it on its own, including Lean proofs of the divsteps design. Circuit design is only one part of a useful quantum computer. Qubits are fragile, so the machine must also catch and fix errors while it runs, which depends on codes, fast decoders, and hardware control that are usually designed separately. The authors say that if design gets faster, useful quantum computing could arrive sooner. That is their suggestion, not a date.