In a research post published October 16, 2026, Anthropic reported that its Claude Mythos 5 model, working in a closed loop with an automated evaluator and largely on its own, designed quantum circuits that improve on the best previously published circuits across eight computational primitives, in some cases by an order of magnitude or more.
The primitives, the basic routines from which larger quantum algorithms are built, span chemistry, optimization, quantum simulation, number theory, and numerical computing. Andi Gu led the work as part of Anthropic’s STEM Fellows Program, with mentorship from Alek Kemeny, a quantum physicist at Anthropic, and in collaboration with Susanne Yelin of Harvard University and Mikhail Lukin of Harvard University and QuEra Computing.
A companion paper, Discovering state-of-the-art quantum circuits with large language models, was submitted to arXiv on October 15, 2026 by Gu, Kemeny, Yelin, and Lukin and runs 46 pages with 10 figures and six tables. The abstract describes an evolutionary framework in which large language models propose circuit designs and an independent evaluator verifies and scores them. It states that in seven of the eight tasks the discovered circuits significantly reduce both Toffoli and qubit counts relative to the state of the art, and that the eighth task yielded a new reversible architecture for prime-field modular inversion.
A Closed-Loop Design Task
Anthropic said Claude was well suited to the work for three reasons. Quantum circuits can be written as ordinary code, so the model can write, run, and revise designs as programs. The targeted class of algorithms can be tested efficiently for correctness, because each input gives one definite output that a conventional computer can check. And the score, the number of qubits multiplied by the number of gates, gives an objective target that serves as a proxy for how long a circuit would take to run. Working in that closed loop, Claude Mythos 5 proposed designs in Python, received correctness feedback and a score from the evaluator program, and revised, with no human input between rounds.
The post describes two constraints that distinguish quantum circuits from ordinary programs. A circuit cannot make if-then decisions, because it runs on a superposition of many inputs at once and must include the operations for every path each time it runs. It also cannot discard information, because every step must be reversible; intermediate results must be stored or “uncomputed” by running the computation that created them in reverse, at the cost of additional gates. Together, these constraints force a trade-off between qubit count and runtime.
As an illustration of what circuit redesign can achieve, the post recounts cost estimates for simulating FeMoco, the iron–sulfur cluster at the heart of nitrogenase, the enzyme bacteria use to convert nitrogen from the air into ammonia. In 2017, researchers estimated that computing FeMoco’s ground-state energy would require about 50 trillion Toffoli gates, one of the most expensive gate types to run and therefore a standard way to estimate how long a quantum computation will take.
A series of algorithmic advances brought the estimate for the same 54-orbital model to about 340 million, a roughly 150,000-fold reduction that the post says corresponds to a few hours of computation on a future machine with about three million physical qubits. Today’s quantum computers have only hundreds to thousands of qubits, and those qubits are highly sensitive to environmental noise.
A Reversible Modular-Inversion Algorithm
The first discovery the post details concerns point addition, the rule for combining two points on an elliptic curve to produce a third. Point addition is the core step in quantum algorithms for the elliptic-curve discrete logarithm problem and one of the field’s standard benchmarks; most of its cost comes from a single step, modular inversion, the wraparound version of division used in elliptic-curve arithmetic. Claude received a one-paragraph brief explaining the mathematical rule and how the evaluator would check and score each design, then worked for 53 hours with minimal human input, limited to the brief and occasional prompts to think more broadly, before arriving at a completely new approach, Anthropic reported.
Classical computers perform modular inversion efficiently using a method called divsteps, but the method had not yielded a practical quantum circuit. Reversibility forces the circuit to retain a record of which operation was chosen at each iteration, called branch information, and storing that history requires an enormous number of additional qubits. Claude reasoned that the record might not need to be stored at all, because the branch information could be decoded by inspecting the pair of numbers after each iteration.
Early candidate decoding rules worked on small test cases but failed at the full 256-bit problem size. Claude then proved a series of results about the iteration, including several new algebraic identities, derived a precise decoding formula, checked it in large-scale numerical simulations, and formalized the claim in Lean. With validation complete, it produced what Anthropic described as the first reversible implementation of divsteps with no stored branch history.
Because decoding saves qubits but costs time, Claude varied the threshold at which the circuit stores rather than decodes the branch information, producing a family of designs between the two extremes. One circuit in the family uses 12% more qubits but 17x fewer gates than the smallest previous design, and the post states that the new designs expand the Pareto frontier of qubit-versus-runtime combinations. The best previously published designs listed for comparison are Schrottenloher (2026) and Luo et al. (2026).
A 12X Cheaper Decoder for Quantum Optimization
The second discovery concerns decoded quantum interferometry (DQI), which the post describes as one of the strongest candidates for a superpolynomial quantum speedup. The algorithm’s most expensive step is an error-correcting decoder, and the researchers who introduced DQI demonstrated it on the optimal polynomial intersection (OPI) problem, a grid-based version of curve fitting, using a Reed–Solomon decoder. Estimates by Google Quantum AI researchers cited in the post imply that solving one particular OPI problem would take about three months on the Frontier supercomputer, compared with roughly an hour on a future quantum computer running DQI, and that most of that hour would be spent on Reed–Solomon decoding.
The previous state-of-the-art circuit processed syndromes, compact summaries of errors, using the extended Euclidean algorithm, in which the number and order of steps depend on the input. Because a quantum circuit handles many inputs with a single fixed sequence of gates, that design had to stretch the computation over more rounds than any single input would need and run every operation in every round. Claude instead organized its circuit around Berlekamp–Massey decoding, which performs the same kind of step in every round and always runs the same number of rounds.
Making that method reversible created a storage problem: temporary values calculated in each round must be recoverable so they can be uncomputed later, and reserving memory for the worst case, an exceptional value arising in 35 different rounds, would take 665 qubits. Claude wrote a high-speed simulator and ran 403 million sample decodings to measure how often such exceptions occur; almost every run needed to save at most one value, so the circuit reserves 19 qubits for a single saved value.
About one run in 10,000 needs more than that and fails, which the post states is well within the error rate the task allows. The post reports that together, the optimizations reduced the decoder’s gate count by a factor of 12 relative to Google’s previous construction, through changes at three levels: the method, the circuit architecture, and the resource budget.
Limitations and Stated Outlook
Anthropic reported that in early experiments Claude was conservative, repeatedly second-guessing apparent improvements, double- and triple-checking well-supported results, and preferring existing, well-known approaches. The caution was sometimes valuable, the post notes, and prompted the Lean proofs that verified the divsteps design. The team took two mitigations: requiring Claude to propose several qualitatively different approaches developed in parallel, and occasionally prompting it to broaden its search.
The post contrasts the 150,000-fold FeMoco reduction, which it says took many research groups eight years, with the single 53-hour run behind the elliptic-curve design. Anthropic stated that the results suggest AI can support the work of circuit design, and raised the possibility that AI could jointly optimize the components of an error-corrected quantum computer, from the algorithm down to the hardware, for a specific problem. The post thanks Arjun Kar and Vinay Ramasesh for helpful discussions in the project’s early stages.
