October 18, 2026

This week, Anthropic published the results of an experiment in which a language model independently designed quantum circuits. The model was given natural-language descriptions of eight computational primitives, an automated evaluator, and the ability to work without human involvement between iterations. In seven of the eight cases, the model produced circuits that outperformed the best published solutions. In some cases, the improvement was an order of magnitude or more. In the eighth case, the model constructed a design that did not appear in the literature.

The same week also saw Google publish a result in quantum error correction.

Publication and Research Participants

• The work was released as part of Anthropic's Stem Fellows program. The preprint was posted on arXiv on October 15, 2026. The paper is 46 pages long. Title: "Discovering state-of-the-art quantum circuits with large language models".
• Lead author: Andy Gu, a program fellow.
• Scientific supervisor: theoretical physicist Alek Kempeni.
• Co-authors: Suzan Jelen and Mikhail Lukin from Harvard University.
• On October 16, Anthropic published its own article on designing more efficient quantum circuits with Claude.

All figures presented in the article are taken from Anthropic's publications or from the preprint itself. Independent replication has not yet been carried out.

Method

The system consists of three components:

1. Generator. Claude receives the specification of a computational primitive and proposes a circuit in Python.
2. Evaluator. A separate program, not another language model, checks the circuit's correctness and computes its quality.
3. Loop. The result is returned to the generator, which revises the circuit. The loop repeats without human involvement between iterations.

The score is calculated as the number of qubits multiplied by the number of quantum gates. This metric roughly corresponds to the circuit's runtime.

Anthropic reports that Claude carried out the design work mostly on its own.

The authors explain why quantum circuits were chosen:

• The evaluator is independent of the generator, so a plausible-looking but incorrect circuit receives a zero score.
• The goal is expressed as a number, so the model can see whether a revision helped.
• Quantum circuits have strict, inexpensive, and automatic correctness checks.

A similar principle is applied in the test suites that govern programming agents.

Eight primitives cover chemistry, optimization, quantum simulation, number theory, and numerical computation.

Features of Quantum Circuits

Quantum circuits impose two constraints that classical programs do not have.

• No conditional branching. A classical program chooses branch A or B. Because of superposition, a quantum circuit must contain operations for every branch in every run.
• Inability to discard data. Every step must be reversible. Erasing auxiliary values contaminates the result. The only way to clean up is to run the computation in reverse, which requires additional gates. A trade-off arises between the number of qubits and the number of steps, which has no direct classical analogue.

Circuit compression matters because current hardware is imperfect. Today's machines contain from several hundred to several thousand qubits and are very sensitive to errors. A slight rise in temperature, weak vibration, and even cosmic rays cause failures. The accumulation of errors renders the result unusable.

Tasks such as breaking ciphers, developing new drugs, and creating room-temperature superconductors require circuits with a minimal number of qubits and a minimal execution time.

Results

Binary Inversion (Divstep)

The main result concerns modular inversion in prime fields. Elliptic curve cryptography relies on point addition, the most expensive part of which is modular inversion.

Classical computers perform it quickly using the divstep algorithm. At each step, the algorithm alternately swaps, adds, or subtracts numbers and divides them by two. In doing so, it generates information about branching and discards it.

A quantum computer cannot discard intermediate data. Preserving the full branching history would require an impractically large number of qubits. For this reason, the earlier version of divstep was considered impractical for reversible integer arithmetic.

Claude's approach was as follows: rather than storing the branching history, reconstruct it by running backward from the final results.

• The model first selected rules blindly. They stopped working once the numbers reached six bits.
• The model then switched to analysis. It studied how the divstep iterations change, proved a set of new algebraic identities, and on that basis wrote an exact decoding rule.
• The rule was formally verified in the Lean system.

The authors claim that this is the first reversible implementation of divstep without a stored branching history. By their estimate, the result shifts the Pareto frontier for the entire family of schemes. One of the new variants uses 12% more qubits but has 17 times fewer gates than the most compact of the previous ones.

According to the authors, this result allows a compiler with a surplus qubit budget to reduce the gate count.

Elliptic Curve Point Addition

According to Anthropic, Claude received initial instructions and, apart from them, only occasionally received additional hints. During a single continuous run lasting 53 hours, the model found a new approach. It:

• proved algebraic identities;
• verified the formulas through large-scale numerical simulations;
• formalized the theorem in Lean.

Formal verification rules out treating the result as merely plausible but unconfirmed.

Reed–Solomon Decoding

Decoded quantum interferometry (DQI) is an optimization algorithm. It is applied to problems in logistics, scheduling, and materials design. The most expensive step of the algorithm is the Reed–Solomon decoder.

Google's previous construction used the extended Euclidean algorithm. Since quantum circuits cannot contain branching, this algorithm had to be unrolled over a large number of rounds.

Claude proposed switching to Berlekamp–Massey decoding. This algorithm performs the same operation in every round. However, this approach introduced a memory problem. Each round leaves behind temporary data that is needed to undo the computations. Handling exceptional cases in the worst case across all 35 rounds would require five qubits.

The model applied the same reverse-execution technique to free up most of the memory. Only a few outliers remained. Reserving a substantial amount of memory for them would have been safe, but the model chose a different path:

• it wrote a fast simulator;
• it ran 403 million trial decodings to determine the frequency of outliers;
• it established that in almost all cases a single value is sufficient;
• it reserved 19 qubits;
• it accepted that roughly one run in 10,000 will require more resources and fail. According to the authors, this falls within the acceptable error budget.

The outcome: the decoder uses 12 times fewer gates than Google's decoder.

According to estimates by Google Quantum AI, solving one OPI problem on the Frontier supercomputer would take about three months. On a future quantum computer running the DQI algorithm, the same task takes about one hour. Most of that hour is spent on Reed–Solomon decoding, so the twelvefold reduction applies to the главная component of computation time. Some publications claim that this reduces the hour to a few minutes.

Проверка заявлений

Ряд утверждений о работе требует уточнения.

Кофактор FeMoco. Железо-молибденовый кофактор входит в состав нитрогеназы и играет ключевую роль в производстве удобрений. В 2017 году оценка числа операций Тоффоли, необходимых для его моделирования, составляла около 50 трлн. Новая оценка, приведённая в публикации Anthropic, составляет около 340 млн. Для квантового компьютера с примерно тремя миллионами физических кубитов расчёт занимает несколько часов. Anthropic характеризует это снижение как примерно тысячекратное.

Срок в 8 лет. Китайский новостной сервис Shinch сообщил, что людям потребовалось 8 лет, а Claude справился за 53 часа. Сама Anthropic приписывает снижение числа операций за восемь лет работе многих исследовательских групп. Проект Claude является одним из шагов на кривой, которая уже снижалась. Кроме того, 53 часа относились только к вычислениям для эллиптических кривых.

Восемь из восьми задач. Тот же источник утверждал, что Claude выполнил все восемь задач. На самом деле семь результатов оказались лучше опубликованных, а в одном случае модель предложила новую постановку задачи.

Limitations of the Results

• Baseline values. The paper's own tables were used for comparison. The baselines were the Shota and Lera projects, the work of Luo et al. (2026), and the work of Katar et al. (2025).
• Reproducibility. No one has yet rerun the test environment. Until then, the results remain the authors' claims.
• Model caution. Anthropic acknowledged an error in the model's behavior. At first, it was overly conservative. The model challenged well-founded improvements and checked schemes two or three times when they were probably correct. This caution proved useful once: it prompted a formal proof in Lean for the div steps. Overall, however, it steered the search toward established approaches.
• Structure of the solution. According to Anthropic, the new result arose from the structure of the search. The model explored several qualitatively different approaches in parallel and periodically received momentum to widen the search area. The authors note that developers of complex models with evaluation loops have probably encountered a similar effect. Anthropic considers this parallelism the transferable technique.
• New problem formulation. The paper itself considers the new problem formulation to be the main value of the result. A search that only tunes parameters within a known structure has limitations.

Setting the physics aside, this architecture is a generator module and an independent verifier working toward a shared result. This scheme is typical of serious modern agentic systems. The work is finished when the test passes, not when the result merely sounds plausible. The critic here is impartial: it is not a model with its own opinion but a simulator that accepts or rejects the scheme. If programmatic verification is not possible, a common solution is to use another model in the role of judge.

Model Routing

OpenRouter has published one of the most detailed analyses of this architecture. It describes it as a routing problem:

• a cheap model generates a large number of proposals, while a more powerful model is used only for verification;
• or a panel of models works on a single request.

The service provides access to more than 200 models through a single endpoint. OpenRouter did not design these schemes, yet reproducing the process requires hundreds of rounds of proposing, evaluating, and correcting for each primitive. For this reason, the service recommends automatic failover rather than relying on a single provider over 12-hour searches.

OpenRouter also maintains an archive of AI-related incidents. Each documented incident receives a source, a severity level, a confidence level, and a flag indicating whether it is disputed.

Model Access and Pricing

• Mythos 5 is not publicly available. Access is restricted to verified partners and participants in the verification program. There is no public API.
• Anthropic releases each step of the Frontier series in two versions with identical weights.
• Mythos includes cyber and biological safeguards configured for verified defense professionals.
• Fable operates with the full set of protective mechanisms.
• The public variant is Claude Fable 5. Pricing: $10 per million input tokens and$50 per million output tokens. OpenRouter applies these prices without markup.
• Fable 5.1 is the public counterpart of Mythos 5.1. The cost is the same, but cache reads are 75% cheaper. The context window is 1 million tokens, the maximum output is 128,000 tokens, and the median time to first token is 2 seconds.

Google Research: Magic States

On October 15, Emma Rosenfeld, a researcher at Google Quantum AI, and Craig Gidney, a quantum software engineer at the same company, reported that magic state distillation works in practice on their Willow processor. The method reduced the error rate by about 40 times. The results are published in the journal Science.

Why Magic States Are Needed

Universal quantum computing requires performing a certain set of operations that cannot be carried out on classical computers. Such operations are implemented with the help of magic states, which are prepared in advance in an error-corrected form.

The problem is cost. High-quality, error-corrected magic states require enormous resources. According to some estimates, their production may consume up to 95% of a quantum computer's capacity. After use, the state is irretrievably consumed.

Researchers predicted this problem in 2004, long before quantum information science became an applied engineering discipline. It took 20 years to solve it gradually.

Magic State Cultivation

In 2024, Gidney, Noah Shutty, and Cody Jones developed an idea from the scientific literature and created a cultivation method.

The principle is reminiscent of a filter:

1. A noisy state is introduced into a small region of the chip.
2. Strictly coordinated measurements are performed that detect errors.
3. Failed attempts are discarded.
4. The remaining state becomes very pure and simultaneously adapts to a larger useful encoding.

On paper, the method could significantly reduce the size of the machine needed for practical tasks.

Experimental Verification

Implementation proved more difficult. Rosenfeld observed data that seemed to contradict the laws of physics. After several months of uncertainty, simulations, discussions with colleagues, and consistency checks, she identified the cause. The team's standard measurement methodology contained an erroneous assumption. Noise caused by drift in electronic equipment and temperature fluctuations reduced the reliability of the test results.

The team changed its approach in both the theoretical and engineering parts:

• added additional control to reduce noise;
• developed a new benchmarking methodology that uses the cultivation process to evaluate itself.

The authors claim this has set a new standard in quantum metrology.

Results

• T-states were obtained with record logical accuracy.
• This is the first hardware demonstration of a practical solution to one of the largest bottlenecks in this field.
• The states were transferred from a distance-3 color code to a distance-5 surface code.
• Color codes are a newer error-correction scheme that is well suited to cultivation. Surface codes are a more established method.
• The purified states retained their quality after transfer.

Scaling the method has not yet been proven. Before a useful error-corrected machine capable of solving problems inaccessible by other means can be built, Google still has to overcome many challenges.

Open Questions

• Will independent replication of the results on div steps and DQI be carried out?
• Will the test environment be published? The authors note that the evaluation cycle is reusable, and the circuits serve, to some extent, as a demonstration of the method.
• Will the described pattern appear in tasks where correctness cannot be verified by machine means?
• How does circuit design relate to other elements of a quantum computer? These elements are usually designed separately. Anthropic mentions joint optimization of error correction, compilation, and hardware, but notes that this is a direction of research rather than a finished result.