Claude Designed Quantum Circuits That Beat the Best Published Ones

Anthropic says Claude can now improve the quantum circuits that quantum computing researchers design by hand. In a research post published on October 16, 2026, the company reports that Claude Mythos 5 redesigned eight circuits and found versions needing fewer qubits and fewer gates than the best published designs, "in some cases by an order of magnitude or more." The full paper is on arXiv and the Anthropic post walks through the method.

The headline example is elliptic-curve point addition: a single 53-hour run produced a design with 12% more qubits than the smallest earlier circuit but 17 times fewer gates. This is a result about resource counts on paper, not a quantum computer running Claude's circuits. Still, it fits a pattern we have been tracking, where Anthropic and others push models toward AI for science work that produces checkable results rather than chat answers.

TL;DR: what Anthropic reported

How did the Claude quantum circuit loop work?

The setup is a closed loop with no human between rounds. Claude writes a circuit design in Python. An automated evaluator checks that the circuit computes the right answer and returns a score. Claude reads the score and revises its next attempt.

Anthropic explains why this task suits a language model. Circuits can be written as code, and for the class of algorithms involved, correctness can be checked efficiently. That makes the problem look like the other domains where models improve fastest: there is a cheap, trustworthy scorer. The same logic sits behind other verifiable-reward successes, such as the OpenAI integer multiplication proof checked in Lean.

The objective was qubits multiplied by gates. Qubits are the scarce hardware resource and gates are the operations that cost time, so their product is a rough proxy for how long a computation would run on a real machine.

Anthropic's research post charts Claude's designs against the best published circuits across all eight tasks.

Anthropic's Figure 2, above, plots the eight tasks, which span chemistry, optimization, physics simulation, number theory and numerical computing. Gray marks are the best previously published designs and orange marks are Claude's. The point addition task is compared separately in a table in the original post.

Why does circuit design matter for useful quantum computers?

Anthropic opens with a historical example. A 2017 estimate put the cost of computing the ground-state energy of FeMoco, a molecule central to nitrogen fixation, at about 50 trillion Toffoli gates. Later algorithmic advances brought that to roughly 340 million gates, a reduction of about 150,000 times. That corresponds to a few hours on a future machine with about three million physical qubits.

The post stresses that those gains came mainly from smarter circuits, not better hardware. If a model can find similar savings faster, the date at which a quantum machine does something useful could move up. In Anthropic's words: "If AI can speed up that work, useful quantum computing could arrive sooner." That is a hope, not a demonstrated timeline, and we treat it as the lab's framing.

For context on the hardware side, see our coverage of Google Willow's magic state cultivation result, which attacks the same bottleneck from the error-correction end.

What did Claude find for elliptic-curve point addition?

Elliptic-curve point addition is a core building block in quantum attacks on elliptic-curve cryptography, so its cost matters for estimates of when such attacks become feasible. Claude worked for 53 hours from a single-paragraph brief and explored several approaches in parallel.

The obstacle was modular inversion. A classical method called divsteps normally stores a long record of branch decisions. In a reversible quantum circuit, that record needs many extra qubits. Claude's key idea was to decode the branch history from the numbers themselves after each iteration, so the record never has to be stored.

Claude derived the algebraic identities that make this work, checked them with large-scale simulations, and formalized the claim in Lean. The result is a family of designs that expands the trade-off frontier between qubits and gates. The most striking point on it uses 12% more qubits than the smallest previous design and needs 17 times fewer gates.

Anthropic compares against two 2026 papers, by Schrottenloher and by Luo and colleagues, which are linked from its post. We have not independently re-run the circuits, so the 17x figure is Anthropic's reported result against those published baselines.

How did Claude shrink the DQI decoder by 12x?

Decoded quantum interferometry, or DQI, is a leading candidate for a superpolynomial quantum speedup on optimization problems. The team focused on a problem called optimal polynomial intersection. Think of it as discrete curve fitting: each column has several acceptable values, and the goal is to find a polynomial passing through as many acceptable values as possible. Google Quantum AI estimates that one instance would take about three months on the Frontier supercomputer but roughly an hour on a future quantum computer running DQI.

The bottleneck is the Reed-Solomon decoder. Claude replaced the extended Euclidean algorithm with Berlekamp-Massey decoding, which runs the same steps every round and so suits a fixed sequence of gates.

Anthropic's post draws three Reed-Solomon decoder locator designs to scale, showing that Claude's circuit needs only a 19-qubit saved value.

A naive reversible version of Berlekamp-Massey has to store a 12-qubit record every round, adding up to 840 qubits. Claude's circuit reconstructs most temporary values from the circuit's current state instead. Worst-case storage would have needed 665 qubits, so Claude used simulation, 403 million sample decodings, to show that a single saved value of 19 qubits is enough.

The price is a small failure probability: about one run in 10,000 fails, which Anthropic says is within the task's allowed error rate. Together the changes cut the decoder's gate count by about 12 times relative to Google's earlier construction. Read that as a trade a human designer might also have made, but the loop found it, tested it and quantified the risk.

What are the limits and open questions?

Anthropic is candid about several limits.

• Conservatism. Claude often second-guessed apparent improvements and repeatedly double- or triple-checked well-supported results. That sometimes helped, for example by prompting the Lean proofs, but it also made the model prefer familiar approaches. The researchers required several qualitatively different approaches and occasionally pushed Claude to broaden its search.
• Scope. Circuit design is only one part of a useful quantum computer. Error correction, fast decoders and hardware control matter too and are usually designed separately. The authors suggest AI could eventually optimize the whole stack jointly, from algorithms down to hardware, but that remains a possibility.
• Failure rate. The DQI design has a small, acknowledged failure probability.
• Verification burden. The evaluator only checks what it was built to check. Anyone adopting these circuits should confirm the specification matches the real application.

We could not find independent replication yet, which is normal on publication day. The paper and the baseline papers are public, so quantum-algorithm researchers can test the claims directly.

What does this mean for people who build with AI?

Three practical takeaways stand out.

1. Verifiable scorers unlock long autonomous runs. A 53-hour run with no human in the loop only worked because the evaluator was trustworthy. If you build agents, the lesson is to invest in the checker first. Our guide to always-on agent architecture covers the loop side.
2. Formal proof is becoming part of the toolchain. Claude used Lean to back up its algebraic claims. The same pairing shows up in math, covered in our post on the Simons Foundation AI math initiative.
3. Science tasks are a growth area for frontier models. Anthropic's recent life-sciences work, such as the verification program around FlashPairFormer, and Nature-level work on AI designing physics experiments point the same way.

If you want to understand the model behind the work, our Fable 5 and Mythos 5 launch post covers where Mythos 5 sits in Anthropic's lineup.

Why the cryptography angle deserves care

Because elliptic-curve point addition is a building block of quantum attacks on elliptic-curve cryptography, cheaper circuits lower the estimated resources for such attacks on paper. That does not mean today's encryption is broken. Large fault-tolerant quantum computers do not exist, and the overall cost of an attack depends on error correction and hardware, which this work does not address. It does reinforce the case for moving to post-quantum cryptography on a planned schedule rather than waiting. Security teams should treat resource estimates as moving targets and watch for follow-up papers that combine these circuits with the latest error-correction overheads.

Bottom line

Anthropic's post is a credible example of a model doing real research-grade optimization in a domain with a cheap, exact scorer. The numbers are large, the method is described in detail, the code-checkable parts were verified, and the limits are stated. What remains is independent replication and, much later, hardware that can run the circuits. We will update this post if outside researchers confirm or dispute the results.

Related reading

• Claude Science: AI workbench for scientists
• Google Willow magic state cultivation, 40x fewer errors
• OpenAI integer multiplication proof in Lean: claimed vs verified
• Simons Foundation AI math initiative
• Nature: AI designing physics experiments
• Anthropic life sciences verification program
• Claude Fable 5 and Mythos 5 launch
• Official: Anthropic research post and arXiv paper

Details are accurate as of October 16, 2026 and reflect Anthropic's own account of its results.