Claude Mythos 5 Helped Design a Quantum Circuit for Bitcoin's secp256k1 Curve: What arXiv 2610.22367's '17-Fold Fewer Gates' Is Measured Against

What Harvard and Anthropic posted on 15 October 2026

Andi Gu, Alek Kemeny, Susanne Yelin and Mikhail Lukin posted arXiv 2610.22367, "Discovering state-of-the-art quantum circuits with large language models," on 15 October 2026. The paper uses Claude Mythos 5 to propose circuit designs and an independent evaluator to test and score them across eight tasks. Anthropic presented the work on 16 October. The result that drew attention is a reversible point adder over the prime field of secp256k1, the curve behind Bitcoin and Ethereum signatures. The authors' public repository lists it at 4,006,673 Toffoli gates and 935 logical qubits, and press coverage reported about 17-fold fewer Toffoli gates for 12% more qubits.

What the 17-fold figure is measured against

The comparator is the authors' own reconstruction of a 2026 point adder by Luo and colleagues, at 69,529,757 Toffoli gates and 838 qubits. The same repository cites a second published design, by Schrottenloher, at about 1.9 million Toffoli gates and 1,446 qubits. Against that design the new circuit uses more gates and about a third fewer qubits. The repository's implemented circuits were evaluated by a grader that runs 100,000 tests and passes a circuit with up to 20 failures, a budget the authors set so that deliberately approximate arithmetic is allowed; the Schrottenloher figures are cited there, not reproduced. This post sets each claim beside the paper and repository, explains what a cheaper adder means for elliptic-curve cryptography, and shows where the figure is commonly overstated.