Anthropic Says Claude Mythos 5 Designed Quantum Circuits That Beat the Best Published Designs

Anthropic says its Claude Mythos 5 model has designed quantum circuits that improve on the best previously published designs across seven of eight computational tasks, in some cases by an order of magnitude or more. The claim, laid out in a research post published Friday and a 46-page paper submitted to arXiv on October 15, is the lab's most concrete demonstration yet that large language models can produce original scientific designs rather than summarize existing knowledge.

The work was led by Andi Gu through Anthropic's STEM Fellows Program, with mentorship from Anthropic quantum physicist Alek Kemeny and in collaboration with Harvard physicists Susanne Yelin and Mikhail Lukin, who is also a founder of quantum computing company QuEra. The paper, titled "Discovering state-of-the-art quantum circuits with large language models," runs 46 pages with 10 figures and six tables, according to Unite.AI, which was among the first outlets to report the results in detail alongside The Quantum Insider and Interesting Engineering.

The eight tasks are computational primitives — the basic routines from which larger quantum algorithms are built — spanning chemistry, optimization, quantum simulation, number theory, and numerical computing. According to the paper's abstract, in seven of the eight tasks the discovered circuits significantly reduce both Toffoli gate counts and qubit counts relative to the state of the art, while the eighth yielded an entirely new reversible architecture for prime-field modular inversion.

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How the Closed Loop Works

The design process is an evolutionary loop in which the language model proposes circuits and an independent evaluator checks them. Quantum circuits can be written as ordinary code, so Claude Mythos 5 submitted designs as Python programs, received correctness feedback and a score from the evaluator, and revised — with no human input between rounds.

The score is deliberately simple: the number of qubits multiplied by the number of gates. That product serves as a proxy for how long a circuit would take to run on a future quantum computer, and it gives the model an objective target to push down.

Quantum circuits also impose constraints that ordinary software does not. A circuit cannot branch on if-then decisions, because it executes on a superposition of many inputs at once and must contain the operations for every path each time it runs. It cannot discard information either, since every step must be reversible — intermediate results must be stored or "uncomputed" by running the computation that produced them in reverse, at a cost in additional gates. Those constraints force a trade-off between qubit count and runtime, which is precisely the trade-off Claude's designs reshaped.

A 53-Hour Run Produces a New Modular Inversion Algorithm

The first detailed discovery concerns point addition, the core operation in quantum algorithms for the elliptic-curve discrete logarithm problem and one of the field's standard benchmarks. Most of its cost sits in a single step — modular inversion, the wraparound version of division used in elliptic-curve arithmetic.

According to Anthropic's post, Claude received a one-paragraph brief explaining the mathematical rule and how the evaluator would score each design, then worked for 53 hours with minimal human intervention before arriving at a genuinely new approach. Classical computers handle modular inversion efficiently with a method called divsteps, but that method had never yielded a practical quantum circuit, because reversibility forces the circuit to record which operation was chosen at each iteration — and storing that branch history requires an enormous number of additional qubits.

Claude's insight was that the record might not need to be stored at all: the branch information could be decoded later by inspecting the pair of numbers produced at each iteration. Early decoding rules worked on small test cases but failed at the full 256-bit problem size, the post states. The model then proved a series of new algebraic identities about the iteration, derived a precise decoding formula, validated it in large-scale numerical simulations, and formalized the claim in the Lean proof assistant.

The result, Anthropic says, is the first reversible implementation of divsteps with no stored branch history. Because decoding saves qubits but costs runtime, Claude produced a family of designs along the frontier between the two. One circuit in that family uses 12% more qubits but 17 times fewer gates than the smallest previous design; the post names the best prior published designs as Schrottenloher (2026) and Luo et al. (2026).

A 12x Cheaper Decoder for Quantum Optimization

The second discovery targets decoded quantum interferometry (DQI), described in the post as one of the strongest known candidates for a superpolynomial quantum speedup. The algorithm's most expensive step is an error-correcting decoder, and estimates by Google Quantum AI researchers cited in the post imply that a particular instance of the optimal polynomial intersection problem would take about three months on the Frontier supercomputer versus roughly an hour on a future quantum computer — with most of that hour spent on Reed–Solomon decoding.

The previous state-of-the-art decoder circuit was built on the extended Euclidean algorithm, whose step count depends on the input, forcing a quantum circuit to stretch the computation over the worst case and run every operation in every round. Claude instead organized its circuit around Berlekamp–Massey decoding, which performs the same work every round. Making that reversible created a memory problem, which the model solved statistically: it wrote a high-speed simulator and ran 403 million sample decodings to measure how often exceptional values occur. Almost every run needed to save at most one value, so the circuit reserves 19 qubits instead of the 665 a worst-case design would require, with roughly one run in 10,000 failing — a rate the post says is well within the task's error budget. The optimizations cut the decoder's gate count by a factor of 12 relative to Google's previous construction, through changes at the method, architecture, and resource-budget levels.

Why It Matters — and What It Doesn't Prove

To illustrate the stakes, Anthropic's post recounts the history of FeMoco, the iron–sulfur cluster at the heart of nitrogenase, the enzyme bacteria use to turn nitrogen into ammonia. In 2017, researchers estimated that computing FeMoco's ground-state energy would require roughly 50 trillion Toffoli gates; a series of algorithmic advances over eight years brought the estimate to about 340 million — a 150,000-fold reduction that corresponds to a few hours of computation on a future machine with around three million physical qubits. The contrast the company draws is blunt: that 150,000-fold improvement took many research groups eight years, while the elliptic-curve result came out of a single 53-hour run.

The caveats are equally clear. Today's quantum computers have only hundreds to thousands of qubits, and those qubits are highly sensitive to noise, so these are designs for future hardware rather than demonstrations on working machines. And the results are Anthropic's own claims, albeit backed by Lean proofs, numerical validation, and an independent evaluator; wider peer scrutiny of the arXiv paper is only beginning.

Anthropic also reports an early behavioral pattern worth noting: in initial experiments Claude was conservative, repeatedly double- and triple-checking well-supported results and preferring familiar approaches. The team countered this by requiring several qualitatively different designs in parallel and occasionally prompting the model to broaden its search — the same caution, the post notes, that prompted the Lean proofs in the first place.

The company's stated outlook is that AI could eventually jointly optimize every component of an error-corrected quantum computer, from algorithm down to hardware, for a specific problem. If the results hold up, the paper may be remembered less for any single circuit than for the demonstration that a language model can hold its own in one of computing's most demanding design disciplines.

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