Claude redesigns quantum circuits on its own: 53 hours on point addition, 12x fewer gates in a DQI decoder

Quantum circuit design can now be carried out autonomously by a model in a closed loop: Claude receives a plain-language specification, proposes a circuit, has an external evaluator check correctness and score it by qubit count times gate count, and uses that score to improve its next attempt, with no human input between rounds. Such improvements previously came from research teams rewriting circuits step by step; the FeMoco ground-state estimate fell from about 50 trillion Toffoli gates to about 340 million over eight years, with each step typically representing months of work. Across eight computational primitives in chemistry, optimization, quantum simulation, number theory and numerical computing, Claude's designs used both fewer qubits and fewer gates than the best previously published algorithms, and the gains came from uncovering new structural and mathematical insights rather than fine-tuning existing designs.

Modular inversion, the costliest step of elliptic-curve point addition, was turned into the first reversible implementation that stores no branch history: instead of recording which operation divsteps chose each round, the circuit infers that record directly from the pair of numbers after each iteration. Divsteps is efficient on ordinary computers, but a quantum circuit must be reversible, and a straightforward quantum version was forced to accumulate the full branch history, requiring an enormous number of additional qubits. Claude's simple candidate decoding rules worked on small cases but failed at the full problem size on 256-bit numbers; it then proved a series of algebraic identities about the iteration process, derived a precise decoding formula, checked it in large-scale numerical simulations and formalized the claim in Lean. By varying the threshold at which the circuit stores rather than decodes, it produced a family of designs, one of which uses 12% more qubits but 17x fewer gates than the smallest previous design.

The Reed–Solomon decoding step, the most expensive part of DQI, was redesigned to cut gates by a factor of 12 relative to Google's previous construction, making that step just over an order of magnitude cheaper. The previous design used the extended Euclidean algorithm, whose number and order of steps depend on the input, while a quantum circuit working on many inputs at once must handle all of them with a single fixed sequence of gates, forcing extra rounds and unnecessary operations. Claude switched to Berlekamp–Massey decoding, which performs the same kind of step every round for a fixed number of rounds; for the few exceptional values that could not be reconstructed from the circuit's current state, it ran 403 million sample decodings and found almost every run needed to save at most one value, so the circuit reserves 19 qubits instead of the 665 needed for the worst case, with about one run in 10,000 failing, within the error rate the task allows.

The report covers circuit-design results on the eight computational primitives Anthropic released, plus two concrete cases: elliptic-curve modular inversion and the DQI decoder. The intended readers are researchers in quantum information, chemical simulation and optimization who follow quantum algorithms and AI-assisted design. Circuit design is only one part of building a useful quantum computer; the machine must also catch and fix its own errors as it runs, which depends on error-correcting codes, fast decoders and hardware control. The source raises a possibility: rather than designing each component separately, AI could optimize them jointly, from algorithm down to hardware, to build an entire error-corrected quantum computer tailored to a specific problem and to tell hardware builders which capabilities matter most.

In early experiments Claude was conservative, repeatedly second-guessing apparent improvements, sometimes double- and triple-checking results that were already well supported, and tending to prefer existing well-known approaches over novel ones; the team mitigated this by requiring several qualitatively different approaches in parallel and occasionally prompting a broader search. About one run in 10,000 of the decoder circuit needs more saved values than reserved and fails, which is within the error rate the task allows. The comparison between the FeMoco gate reduction and the elliptic-curve design's runtime comes from the source's own narrative and is not a controlled comparison under one evaluation protocol.