# Claude proposes quantum circuits that reduce estimated gate and qubit costs > An Anthropic and Harvard preprint uses Claude to propose quantum circuits and a separate evaluator to check them. Seven of eight tasks show lower estimated gate and qubit counts under the paper's comparisons. By BIG CHANGE Editorial Published: 2026-10-17T13:44:34.835Z Updated: 2026-10-17T13:44:34.835Z Canonical: https://bigchange.ai/blog/claude-quantum-circuits-gate-qubit-estimates ![Conceptual charcoal illustration of pegs in three channels of a wooden logic model beside a separate measuring gauge.](https://bigchange.ai/api/media/file/quantum-circuit-evaluator-concept-v1.png) AI-generated conceptual illustration by BIG CHANGE; physical analogy, not a circuit from the preprint or a measured result. Researchers working with Anthropic used Claude Mythos 5 to propose quantum circuits, then checked the proposals with a separate program. In a [preprint submitted October 15](https://arxiv.org/abs/2610.22367), they report lower Toffoli gate counts and peak qubit counts than their comparison designs on seven of eight circuit-building tasks. The eighth, prime-field modular inversion, produced a family of different gate and qubit trade-offs. These are estimates for proposed logical circuits, not measurements from a quantum computer. The result is useful to researchers deciding where AI-assisted design may help: the team gave the model a precise function to implement and a fast way to reject incorrect attempts. BIG CHANGE reviewed the paper and Anthropic's October 16 [research account](https://www.anthropic.com/research/designing-efficient-quantum-circuits). We did not run the search, reproduce the resource estimates or execute a circuit on hardware. ## The big change - **What changed:** An evaluator-guided search produced circuit designs for eight specified quantum-computing primitives. The paper reports lower gate and qubit counts on seven tasks, with a different trade-off for modular inversion. - **Why it matters:** A large quantum algorithm repeatedly calls smaller routines. Reducing the resources estimated for those routines could lower the requirements of a future implementation, if the designs hold up when integrated with error correction and hardware constraints. - **What to watch:** Independent scrutiny of the circuit constructions, their stated error budgets and hardware-specific resource estimates will determine how far the results carry beyond these test cases. ## A model proposes; an evaluator checks A quantum circuit has to preserve information that an ordinary program can overwrite. Temporary values must be cleared by reversing the work that produced them, a process called uncomputation. Holding those values occupies qubits; recomputing them costs gates. The [paper](https://arxiv.org/html/2610.22367v1) focuses on routines whose behavior can be stated as a classical function embedded in a reversible quantum operation. That restricted class makes an automated correctness check practical. For each of eight tasks, researchers wrote the required input-output behavior and started the search from a blank program. Claude proposed several algorithm families as Python programs that construct circuits. Separate searches improved each family, periodically sharing strong candidates. The evaluator tested whether a submitted circuit produced the required output, preserved inputs, cleared temporary qubits and handled phase correctly. It then counted Toffoli gates and the maximum number of logical qubits allocated at once. A candidate that failed the task specification was rejected; valid candidates were ranked by the product of the two resource counts. The paper calls this an evolutionary search using OpenEvolve and Claude Mythos 5. Each model iteration received a parent program, feedback and a limited set of alternatives from the archive. The evaluator's results informed the next proposal. Anthropic says a long search on elliptic-curve point addition ran for 53 hours with occasional human prompts to explore more broadly. The initial specifications, choice of tasks and scoring rules were human decisions. ## The reported savings and their conditions The team's [eight-task results table](https://arxiv.org/html/2610.22367v1) covers decoders for an optimization algorithm, numerical functions, a chemistry circuit, lattice-gauge simulation and modular inversion. For the Reed–Solomon decoder, the paper compares a published baseline of 5.1 million Toffoli gates and 1,938 peak logical qubits with a proposed design of 440,000 gates and 1,837 qubits. Its gate-times-qubit score improves by a factor of 12 under the paper's accounting. For a fixed-point Gaussian function, the reported counts move from 24,000 gates and 362 qubits to 1,583 gates and 139 qubits, giving a 39-fold improvement in that score. The eighth task needs a different reading. The authors give no single baseline or improvement factor for prime-field modular inversion because earlier constructions exchange more gates for fewer qubits, or vice versa. Their complete benchmark circuit uses 4.0 million Toffoli gates and 935 logical qubits. A design in the new family uses 12% more qubits than the smallest prior design but 17 times fewer gates, according to Anthropic's account. That is a trade-off, not an across-the-board reduction. One proposed decoder also makes a deliberate reliability trade-off. It reserves 19 qubits for one exceptional stored value instead of 665 qubits for the worst possible sequence of exceptions. The paper estimates that roughly one input in 10,000 would need more storage and fail under its specified distribution. Other tasks use different accuracy or failure criteria. A reader comparing the rows must retain those conditions alongside the gate and qubit counts. ## What the calculation cannot settle The evaluator follows computational-basis inputs through circuits that permit efficient classical simulation. It checks sampled inputs for large domains rather than proving every possible input correct. Some task specifications require exact results, but their reported validation still uses finite test sets. These checks support the reported proposals within each task's stated interface and error tolerance; they do not show a circuit running on quantum hardware. Toffoli count and peak logical qubits are proxies for future time and space costs. A machine's gate depth, routing, error-correction system and physical qubits can change which design is preferable. The authors also fix each task's input representation, leaving some encoding changes outside the search. Those limits matter before applying a promising subroutine to a complete algorithm. The strongest conclusion is about the design method. When a research problem has a clear specification and a sufficiently fast independent evaluator, a model can explore circuit architectures that a simple sequence of local gate rewrites may miss. The specific resource numbers remain the authors' preprint results, awaiting independent reproduction and a hardware-aware assessment. ## Sources & further reading - [Discovering state-of-the-art quantum circuits with large language models](https://arxiv.org/html/2610.22367v1). Andi Gu, Alek H. Kemeny, Susanne F. Yelin and Mikhail D. Lukin, arXiv v1 submitted October 15, 2026. The primary preprint describes the search, evaluator, eight task results, validation and limits. It is a research report, not a hardware deployment. - [Designing more efficient quantum circuits with Claude](https://www.anthropic.com/research/designing-efficient-quantum-circuits). Anthropic, October 16, 2026. The authors' explanation of the research, including the 53-hour point-addition search and the modular-inversion trade-off. Its outlook about future practical quantum computers is a projection, not an observed result. ## Sources - [Discovering state-of-the-art quantum circuits with large language models](https://arxiv.org/html/2610.22367v1) — Primary arXiv v1 preprint: method, eight-task comparison, correctness testing, resource estimates and limits. Research report, not hardware execution. - [Designing more efficient quantum circuits with Claude](https://www.anthropic.com/research/designing-efficient-quantum-circuits) — Authors' explanatory account. Describes the 53-hour search and modular-inversion trade-off; future-computer implications are projections.