Claude Mythos 5 Found Quantum Circuits Better Than the Published Best — Starting With One That Cuts Gates by 17×

A​nthropic's STEM Fellows Program published a result this week in which C​laude M​ythos 5 was handed plain-language specifications for eight quantum circuits and, working in a closed loop against an automated evaluator, returned designs that beat the best published ones on seven of them — and on the eighth produced something the literature did not have: a reversible divsteps implementation with no stored branch history, one member of which uses 12% more qubits but 17× fewer gates than the smallest previous design. The paper, Discovering state-of-the-art quantum circuits with large language models, is on arXiv (2610.22367, submitted 15 October 2026, 46 pages), and its lead author is Andi Gu, a fellow in the program, mentored by quantum physicist Alek Kemeny and working with Susanne Yelin and Mikhail Lukin of Harvard. Every number below is A​nthropic's own or comes from the paper's own tables; none of it has been independently reproduced yet.

What was actually run, and what was not

The setup is worth describing precisely, because the interesting claim is not "a model wrote some code." A​nthropic gave C​laude M​ythos 5 a specification for a computational primitive, and the model proposed a circuit as Python. A separate evaluator — a program, not a model — checked the circuit for correctness and scored it on qubit count multiplied by gate count, a proxy for runtime. The score went back to the model, which revised. There was no human in the loop between rounds. A​nthropic's description is that C​laude worked "largely on its own."

Two things about that loop are doing the heavy lifting. The first is that the evaluator is independent of the proposer, so a plausible-looking wrong answer scores zero rather than winning an argument. The second is that the objective is a number, which means the model can tell whether a revision helped. This is the same shape as a test suite driving a coding agent, and it is the reason A​nthropic picked quantum circuits to study: the domain has a hard, cheap, automatic correctness check.

The eight primitives span chemistry, optimization, quantum simulation, number theory and numerical computing. Two constraints make the domain unusual. Quantum circuits have no if-then branching, because superposition means an operation is needed for every branch; and they cannot discard information, because every step must be reversible. Leftover scratch values have to be uncomputed by running the computation backwards, which costs gates. That forces a space-versus-time trade-off that has no classical analogue, and it is exactly the kind of trade-off a search process can be pointed at.

The four results worth reading in detail

• Divsteps / prime-field modular inversion. This is the headline. C​laude produced the first reversible divsteps implementation that stores no branch history — a construction the paper describes as making divsteps, a classical algorithm previously impractical for reversible integer arithmetic, newly workable. The usable outcome is a Pareto shift rather than a single win: a member of the resulting design family spends 12% more qubits and 17× fewer gates than the smallest previous design, so a compiler with a qubit budget to spare can now buy gates with it.

• DQI / Reed–Solomon decoding. C​laude's decoder cuts the gate count by a factor of 12 against G​oogle's previous construction, partly by swapping the extended Euclidean algorithm for Berlekamp–Massey decoding. The storage detail is the interesting one: worst-case handling of exceptions across 35 rounds would take 665 qubits, and after a simulator ran 403 million sample decodings C​laude instead reserved room for a single value — 19 qubits — accepting that roughly one run in 10,000 needs more and fails, a rate inside the allowed error budget.

• Elliptic-curve point addition. A single 53-hour run with minimal human input — an initial brief plus occasional prompts — produced a new approach. C​laude proved the algebraic identities, tested the formulas in large-scale numerical simulations, and formalised the claim in Lean, which is the kind of self-checking that makes the result harder to dismiss as a plausible-looking artifact.

• The FeMoco trajectory, which needs a caveat. A​nthropic's page sets C​laude's result against the 2017 estimate for simulating the iron–molybdenum cofactor: about 50 trillion Toffoli gates, falling to roughly 340 million, a reduction of some 150,000-fold, which the page describes as a few hours on a future machine with about three million physical qubits. Read that as a field-wide trajectory, not a single result. The page itself attributes the eight-year reduction to many research groups, and the honest reading is that C​laude's design is a step inside a curve that was already falling steeply.

For scale on why the DQI number matters: G​oogle Quantum AI's own estimates imply one OPI problem would take about three months on today's Frontier supercomputer against roughly an hour on a future quantum computer running DQI — and most of that hour goes to Reed–Solomon decoding. Cutting decoder gate count by 12× is a cut to the dominant term.

What "beats the published best" does not mean

Four honest limits, stated before anyone quotes the 17× out of context.

The first is that this is a preprint with no independent reproduction. A​nthropic ran the evaluator; the comparison baselines come from the paper's own tables, with prior designs sourced to Schrottenloher (2026), Luo et al. (2026) and Khattar et al. (2025). The claimed advantage is a claim until someone reruns the harness.

The second is that circuit design is one component of a quantum computer, and the components are usually designed separately. A​nthropic notes the possibility that error correction, compilation and hardware constraints could be optimised jointly by the same method — which is a research direction, not a result.

The third is a failure mode A​nthropic reports against itself: in early experiments the model was conservative, repeatedly second-guessing well-supported gains and double- or triple-checking designs that were probably fine. That caution produced a real benefit once — it prompted the Lean proofs on the divsteps result — but it also biased the search toward established approaches. The mitigation was structural: require several qualitatively different approaches developed in parallel, and occasionally prompt the model to widen its search. Anyone building evaluator-driven loops on any frontier model will recognise that failure mode, and the parallel-approaches fix is the transferable part.

The fourth is that seven of eight tasks produced a better score on an existing formulation and one produced a new formulation. Those are different kinds of result, and the paper's own framing treats the eighth as the interesting one, because a search that only tunes parameters inside a known structure has a ceiling.

The part that generalises beyond quantum computing

Strip the physics out and what A​nthropic built is a proposer and an independent checker, wired together, with a scalar objective that both sides can see. That pattern is now the standard shape of serious agentic work: one model generates, another verifies, and the loop stops when a test passes rather than when the output reads well. The lesson the quantum paper adds is about honesty of the critic — the evaluator here is not a second model offering an opinion. It is a simulator that either accepts the circuit or does not.

Where a program cannot be the judge, the second-best structure is a different model as judge, and that is a routing problem rather than a research one. OrcaRouter's routing DSL composes several models into a single call, so a cheap model can run the high-volume proposer branch while a stronger one is invoked only on the verification step, and model fusion runs a panel of models against the same prompt when a single opinion is not worth trusting. The point is not that a router designed the circuits — it did not, and A​nthropic's loop does not need one. The point is that the loop A​nthropic describes is buildable on a single endpoint across 200-plus models with no second contract, and the cost of the loop is dominated by how many proposer rounds you can afford.

Where you can actually run something like this

C​laude M​ythos 5 itself cannot be called. It is restricted to vetted partners and verification-program members, it does not appear on any public API, and it is not routed here — a gated model cannot be routed to the public. What is reachable is its public sibling. A​nthropic ships every frontier step as two SKUs of the same weights: the M​ythos SKU with cyber and biology safeguards tuned for vetted defenders, and the Fable SKU with the full safeguard stack left on. Claude Fable 5 is the ungated member of C​laude M​ythos 5's generation, and it sits in the OrcaRouter catalogue at A​nthropic's list price of $10 per million input tokens and $50 per million output tokens, passed through at 0% markup, with the newer Claude Fable 5.1 — the public twin of C​laude M​ythos 5.1 — alongside it at the same rate and a 75% lower cache read. That is the practical route to the capability tier the paper is about, and it costs the vendor's own number rather than a marked-up one.

Worth saying plainly: the paper's gains came from a loop, not a single prompt. Anyone trying to reproduce this should budget for hundreds of proposition-evaluate-revise rounds per primitive and pick a model whose cost per round they can live with. That is the argument for putting the loop behind a router with automatic failover, rather than betting a twelve-hour search on one provider having a good afternoon.

What to watch next

Three checkable things. An independent rerun of the evaluator on the divsteps and DQI circuits, which is the only way the 17× and 12× become more than A​nthropic's numbers. Whether the harness itself is released, because the feedback loop is the reusable contribution and the circuits are the demonstration. And whether the same proposer-and-evaluator pattern shows up on a problem where correctness is not machine-checkable, since that is where the model-as-judge question stops being academic.

Until then, the fair summary is that a gated frontier model, pointed at a domain with a cheap objective function and left alone for 53 hours, moved a resource frontier that human researchers had been pushing at for eight years. That is worth taking seriously on the strength of the method even while the specific multipliers stay labelled as the vendor's own.

None of that is hypothetical: the documented AI failures and agent incidents behind releases like this one are collected in the OrcaRouter AI Incident Archive, where each entry carries its own sources, severity, confidence grade and disputed flag.