Quantum circuits designed by Claude: up to 17x fewer gates

On October 16, 2026, Anthropic described how Claude Mythos 5 designed quantum circuits for eight tasks spanning chemistry, optimization, physical simulation and number theory. According to the paper on arXiv, in seven of them the circuits it found clearly cut both the Toffoli gate count and the qubit count compared with the best known constructions. The study was done by Andi Gu from Anthropic’s STEM Fellows program, quantum physicist Alek Kemeny, and Susanne Yelin and Mikhail Lukin from Harvard (Lukin also works with QuEra Computing).

Why do quantum circuits matter so much?

Future quantum computers will have very limited hardware, so whether an algorithm can run at all comes down to circuit design. Anthropic gives an example from chemistry: in 2017, computing the ground-state energy of the FeMoco cofactor was estimated at around 50 trillion Toffoli gates. Today the same model (54 orbitals) needs around 340 million, roughly 150,000 times fewer.

Interestingly, most of that drop came not from better hardware but from smarter circuits. And that is exactly the stage Claude tried to speed up.

How did Claude design the circuits?

Claude got a plain-language description of the task and worked in a closed loop: it proposed a design, and an independent evaluator checked it for correctness and scored its cost as qubit count times gate count. There was no human involvement between rounds. The authors call it an evolutionary approach: the model proposes variants, and the evaluator verifies and scores them.

It’s a simplified metric (it doesn’t directly tell you how long the circuit will run), but it lets designs be compared automatically.

What exactly got better?

Anthropic describes two results in detail:

1. Elliptic curve point addition. This is a standard benchmark for quantum discrete logarithm algorithms, the ones that could one day threaten elliptic curve cryptography. Claude built a reversible version of the divsteps algorithm for modular inversion and, instead of storing the branch history, read it back from the numbers themselves. One of the designs has 12% more qubits but 17x fewer gates than the smallest previous design. The work took Claude 53 hours, and it formalized one of the theorems in Lean.
2. A decoder for DQI (decoded quantum interferometry). DQI is a candidate algorithm with a superpolynomial speedup, and its most expensive step is decoding Reed–Solomon codes. Claude based the circuit on the Berlekamp–Massey algorithm and recomputed most intermediate values instead of storing them. Reserving room for the worst case would have required 665 qubits. After 403 million trial decodings, it turned out that a single stored value (19 qubits) is enough, and an error occurs roughly once in 10,000 runs, which is within the acceptable limit. The result: 12x fewer gates than Google’s earlier construction.

For scale: Google estimates that one optimal polynomial intersection problem would take about three months on the Frontier supercomputer, and roughly an hour on a future quantum computer running DQI.

Does this mean quantum computers are just around the corner?

No. These are better circuit designs, not new hardware. Even the optimized FeMoco computation would, according to Anthropic, take a few hours on a future machine with around three million physical qubits, and no such machine exists today.

The authors are also open about the weaknesses: Claude was conservative and often re-checked what it already had several times. What helped was asking it to explore several qualitatively different approaches in parallel and to widen the search from time to time. Still, the result is impressive: a language model in a closed loop is breaking records in a field specialists have worked on for years.

It’s also another example in recent days of Mythos-family models landing in serious research and security work (I wrote earlier about how Claude Mythos forced Bank of America to patch flaws).

FAQ

Who designed these quantum circuits?

Claude Mythos 5, working in a closed loop with an automated evaluator. The study was led by Andi Gu from Anthropic, together with Alek Kemeny, and Susanne Yelin and Mikhail Lukin from Harvard.

Did Claude break elliptic curve cryptography?

No. It improved the circuit for curve point addition, which is a building block of future quantum algorithms. Running them requires a large quantum computer, and none exists today.

What is a Toffoli gate?

An expensive logic gate that acts on three qubits. The Toffoli gate count serves as a rough measure of how much work a quantum computer has to do.

Where can I read the paper?

On arXiv: “Discovering state-of-the-art quantum circuits with large language models”, published October 15, 2026.