Anthropic says Claude beats best published quantum circuit designs

In a research post published on 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 previously published best circuits across eight computational primitives, in some cases by an order of magnitude or more.

Primitives, the basic routines from which larger quantum algorithms are built, range from chemistry, optimization, quantum simulation, number theory, and numerical computation. Andi Gu led the work as part of Anthropic’s STEM Fellows program, with guidance from Anthropic quantum physicist Alek Kemeny, 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 comprises 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 is claimed that in seven of the eight tasks the discovered circuits significantly reduce both the Toffoli number and the qubit number compared to the state of the art, and that the eighth task produced a new reversible architecture for modular prime field inversion.

A closed-loop design task

Anthropic said Claude was right for the job for three reasons. Quantum circuits can be written like ordinary code, so the model can write, execute and review designs like programs. The target class of algorithms can be efficiently tested for correctness, since each input provides a defined output that a conventional computer can control. And the score, the number of qubits multiplied by the number of gates, provides an objective target that acts as a proxy for how long it would take a circuit to run. Working in this closed loop, Claude Mythos 5 proposed projects in Python, received feedback on correctness and a score from the evaluation program, and revised them, without 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 operates on a superposition of many inputs at once and must include operations for each path every time it is executed. It also cannot discard information, because each step must be reversible; intermediate results must be stored or “uncalculated” by running the calculation that created them in reverse, at the cost of additional checks. Together, these constraints impose a trade-off between qubit count and runtime.

To illustrate what the circuit redesign can achieve, the post recounts cost estimates for simulating FeMoco, the iron-sulfur cluster at the heart of nitrogen, the enzyme used by bacteria to convert nitrogen in the air into ammonia. In 2017, researchers estimated that calculating FeMoco’s ground-state energy would require around 50 trillion Toffoli gates, one of the most expensive types of gates to operate and therefore a standard way to estimate how long a quantum calculation will take.

A series of algorithmic advances have brought the estimate for the same 54-orbital model to about 340 million, a reduction of about 150,000 times which, according to the post, corresponds to a few hours of computation on a future machine with about three million physical qubits. Today’s quantum computers only have hundreds to thousands of qubits, and those qubits are highly sensitive to ambient noise.

A reversible modular inversion algorithm

The first discovery detailed in the post concerns point addition, the rule for combining two points on an elliptic curve to produce a third. Point addition is the fundamental step in quantum algorithms for the elliptic curve discrete logarithm problem and one of the industry standard benchmarks; most of its cost comes from a single step, from 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 project, then worked for 53 hours with minimal human input, limited to brief, occasional prompts to think more broadly, before arriving at an entirely new approach, Anthropic reported.

Classical computers perform modular inversion efficiently using a method called divsteps, but the method had not produced a practical quantum circuit. Reversibility forces the circuit to keep a record of which operation was chosen at each iteration, called branch information, and storing that history requires a huge number of additional qubits. Claude thought that perhaps it was not necessary to memorize the record, because the branch information could be decoded by examining the pair of numbers after each iteration.

The first 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 iteration, including several new algebraic identities, derived a precise decoding formula, verified it in large-scale numerical simulations, and formalized the statement in Lean. Once validation was complete, it produced what Anthropic described as the first reversible implementation of divstep with no branch history stored.

Because decoding saves qubits but costs time, Claude varied the threshold at which the circuit stores rather than decodes branch information, producing a family of designs between the two extremes. One circuit in the family uses 12% more qubits but 17 times fewer gates than the smallest previous design, and the post claims that the new designs expand the Pareto frontier of qubit-versus-runtime combinations. Previously published best projects 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 superpolynomial quantum acceleration. The most expensive step in the algorithm 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 from Google Quantum AI researchers cited in the post imply that solving a particular OPI problem would take about three months on the Frontier supercomputer, compared to about an hour on a future quantum computer with DQI, and that most of that hour would be spent on Reed-Solomon decoding.

Previous state-of-the-art circuitry processed syndromes, compact summaries of errors, using the extended Euclidean algorithm, where 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 extend the computation over more cycles than needed for any single input and perform each operation in each round. Claude instead organized his circuit around the Berlekamp-Massey decoder, which executes the same type of step in each round and always executes the same number of rounds.

Making that method reversible created a storage problem: Temporary values computed in each round must be recoverable so they can’t be computed later, and reserving memory for the worst case, an exceptional value occurring in 35 different rounds, would require 665 qubits. Claude wrote a high-speed simulator and ran 403 million sample decodes to measure how often such exceptions occur; almost every execution required saving at most one value, so the circuit reserves 19 qubits for a single saved value.

About one in 10,000 runs takes more than this and fails, which, according to the post, is well within the error rate allowed by the task. The post reports that, together, the optimizations reduced the number of decoder gates by a factor of 12 compared to Google’s previous build, through changes at three levels: the method, the circuit architecture, and the resource budget.

Stated limitations and prospects

Anthropic reported that in early experiments Claude was conservative, repeatedly doubted obvious improvements, double- and triple-checked well-supported results, and preferred existing, well-known approaches. Caution was valuable at times, the post notes, and led to the Lean trials that verified the divsteps project. The team adopted two solutions: requiring Claude to propose several qualitatively different approaches developed in parallel and, occasionally, pushing him to broaden his research.

The post compares FeMoco’s 150,000-fold reduction, which many research groups say took eight years, to the single 53-hour run behind the elliptic curve design. Anthropic said the findings suggest that artificial intelligence can support circuit design work, and raised the possibility that artificial intelligence could jointly optimize the components of an error-correcting 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 early stages of the project.