What Anthropic says it got
Anthropic published results on 16 October claiming that its Claude Mythos 5 model produced quantum circuits that beat the best designs in the published literature for eight computational primitives, spanning chemistry, optimisation, quantum simulation, number theory and numerical computing.
Two are described in detail in the company’s write-up. The first is elliptic-curve point addition, the inner step of quantum algorithms for the discrete logarithm problem. One of the model’s designs uses 12% more qubits than the smallest previous circuit but 17 times fewer gates. Anthropic says the set of designs widens the frontier of trade-offs between qubit count and runtime, rather than winning on a single number.
The second is Reed-Solomon decoding inside decoded quantum interferometry, or DQI, applied to optimal polynomial intersection. There the model’s circuit cuts the gate count by about 12 times against Google Quantum AI’s previous construction, which Anthropic describes as a little over an order of magnitude cheaper in total.
How the loop worked
Claude wrote each circuit as Python code. An external evaluator checked that the circuit did what the specification required and scored the valid ones by qubit count multiplied by gate count, a proxy for runtime. The score went back to the model, which revised and tried again. Anthropic says no human intervened between rounds.
The point-addition result came out of a single 53-hour run started from a one-paragraph brief, during which the model explored several approaches in parallel. Humans occasionally prompted it to widen its search. For the modular inversion step, Claude built a reversible version of the divsteps algorithm, derived the decoding rule mathematically, checked it against large-scale simulations, and then formalised the claim in Lean.
The decoder result turns on memory. A naive reversible implementation would need up to 840 qubits to hold branch records, and reserving for the worst case would still take 665. Claude’s circuit reserves 19, after a simulator ran 403 million sample decodings to measure how often more is needed. Roughly one run in 10,000 fails for want of space, which Anthropic says sits inside the error budget the task allows.
Why the decoder matters
Google Quantum AI’s own resource estimates make decoding the dominant cost in DQI, so a cut there moves the whole estimate. Anthropic compares its circuits against the published designs it is beating by name: Schrottenloher and Luo et al., both 2026, for point addition, and the extended-Euclidean construction of Khattar et al. from 2025 for the decoder.
What is not claimed
Anthropic does not report running any of these circuits on physical quantum hardware, and does not claim the designs are optimal — only that they beat the best published ones on the stated metric. It gives no numbers in the text for the other six primitives, pointing instead to a figure. It also notes that circuit design is one piece of a working quantum computer, with error correction and hardware control as separate problems, and that faster design “could” shorten the path rather than setting any date.
The company is candid about the model’s temperament, describing it as conservative, inclined to second-guess its own results, and liable to reach for well-known approaches unless told to look further. The widely cited drop in the estimated cost of simulating FeMoco, from roughly 50 trillion Toffoli gates in 2017 to about 340 million, comes from the wider literature and not from Claude’s work.
What to watch
Every figure here is Anthropic’s own, scored by an evaluator Anthropic built. The test is whether anyone outside the company re-runs the evaluator on the divsteps and DQI circuits and gets the same numbers.
