Claude cuts quantum-circuit costs across an eight-task benchmark

Anthropic reports that Claude Mythos 5 designed quantum circuits with lower resource requirements than previously published constructions across eight computational primitives. The research report, produced through Anthropic’s STEM Fellows Program with Harvard researchers Susanne Yelin and Mikhail Lukin, covers chemistry, optimization, physics simulation, number theory, and numerical computing. Lukin is also affiliated with QuEra Computing.

An evaluator closes the loop

Each optimization run followed a repeatable workflow:

1. Claude generated a quantum circuit in Python.
2. An external evaluator checked the circuit’s specified behavior.
3. The evaluator scored valid designs using qubit count multiplied by gate count.
4. Claude received the score and revised its next attempt.

Humans selected the problems, wrote the initial briefs, built the evaluators and scoring functions, and occasionally prompted Claude to widen its search. The proposal, evaluation, and revision cycle then ran without human intervention between individual rounds. Anthropic says the resulting circuit families improved the published resource trade-offs for all eight tasks, including designs that reduced both qubits and gates.

Fixed circuits collide with ordinary control flow

Classical programs can select an instruction path after inspecting an input. A coherent quantum circuit operating on a superposition must encode data-dependent behavior through controlled operations inside one circuit, preserving every possible input state at once. That constraint makes irregular branches expensive.

Quantum computation also preserves information through reversible operations until measurement. Temporary values therefore cannot simply be overwritten while coherence must be maintained. Circuits commonly erase scratch data through uncomputation, which applies the relevant operations in reverse and adds gates. Designers must balance extra qubits for stored intermediates against extra gates for recomputation.

This combination turns circuit design into a constrained search problem with several measurable objectives. A smaller gate count can shorten execution and reduce accumulated error, while fewer logical qubits can lower the physical hardware required for fault-tolerant operation.

Recovering branch history from the numbers

Claude’s largest reported gate reduction came from elliptic-curve point addition, a core operation in quantum algorithms for solving the elliptic-curve discrete logarithm problem. That problem underpins widely deployed public-key cryptography, although present quantum hardware remains far below the fault-tolerant scale required for such attacks.

Modular inversion dominates the cost of point addition. Classical implementations can use divsteps, a fast variant of the extended Euclidean algorithm. A direct quantum translation accumulates the algorithm’s data-dependent branch history so that every step can later be reversed, consuming many additional qubits.

During a 53-hour run, Claude developed a method that reconstructs each earlier branch from the current numerical pair. Anthropic reports that the model derived new algebraic identities, produced a decoding formula for recovering the branch information, tested it with large numerical simulations, and formalized the central claim in Lean, a proof assistant that checks each logical step against a machine-readable specification.

One circuit from the resulting family uses 12% more qubits than the smallest previous construction and 17-fold fewer gates. Other variants occupy different points on the Pareto frontier, where improving either qubit count or runtime would worsen the other measure.

Berlekamp-Massey regularizes the decoder

Claude also redesigned the Reed-Solomon decoder used by Decoded Quantum Interferometry, or DQI. The algorithm has been proposed as a route to a superpolynomial quantum advantage, with the projected separation between quantum and classical costs growing rapidly as problem size increases.

Google Quantum AI’s earlier decoder used the extended Euclidean algorithm, whose control flow varies with the input. Claude rebuilt the decoder around Berlekamp-Massey, an algorithm that recovers algebraic error patterns through a fixed number of structurally similar rounds. Its regular control flow maps more directly onto a fixed quantum circuit.

Claude then reduced memory use by reconstructing intermediate values from the current state. A worst-case allocation for exceptional values arising in 35 rounds would require 665 qubits. To estimate the typical requirement, it wrote a simulator and ran 403 million sample decodings. Almost every sample needed storage for at most one exceptional value, allowing the circuit to reserve 19 qubits. The resulting design fails about once per 10,000 runs, within the task’s permitted error rate, and uses about one-twelfth the gates of Google’s construction.

Resource cuts reshape hardware estimates

Logical resource estimates connect an algorithm to the fault-tolerant hardware needed to run it. Gate reductions can shorten execution, while lower logical-qubit requirements can reduce the number of physical qubits devoted to error correction.

FeMoco simulation illustrates how algorithmic improvements can change those estimates. FeMoco is the active site of nitrogenase and a standard benchmark for quantum chemistry. A 2017 estimate placed its ground-state calculation at roughly 50 trillion Toffoli gates. Subsequent work reduced that estimate to about 340 million gates, an improvement of roughly 150,000-fold. One projection maps the newer design to several hours on a future machine with about three million physical qubits.

A single 53-hour circuit-design run cannot be directly equated with eight years of advances from multiple research groups. The problems, evaluators, and measures differ, and Anthropic selected tasks that could be checked automatically. The experiment nevertheless shows that automated search can produce substantial resource reductions when correctness and cost are available as machine-readable feedback.

What the benchmark leaves open

• Human scaffolding: Researchers chose the tasks, defined correctness, built the evaluators, and supplied the cost function.
• Human steering: The team occasionally asked Claude to explore several qualitatively different approaches, pursue them in parallel, and move beyond incremental revisions.
• Search behavior: Early runs favored established methods and repeatedly questioned valid improvements, requiring prompts that encouraged broader exploration.
• Verification: Lean supported the modular-inversion argument, while other results relied on task-specific checks and large numerical simulations.
• Cost model: Qubit and gate counts capture central logical resources but do not include every expense of compilation, error correction, control hardware, or operation on a physical device.
• Hardware status: The work presents circuit designs and resource estimates, not executions on a fault-tolerant quantum computer.

Anthropic attributes the mathematical constructions and proofs to Claude within this human-built research environment. That division matters when interpreting the work as autonomous research: the model supplied the central circuit ideas, while researchers supplied the questions, tools, incentives, and occasional direction.

From isolated circuits to co-design

Error-correcting codes, syndrome decoders, compilers, and hardware-control systems can often be expressed as code, tested against explicit requirements, and scored on resource use. Anthropic proposes extending the same optimization loop across several layers at once, allowing an agent to co-design algorithms and supporting systems. That remains a research direction rather than a demonstrated result.

Developers and researchers can inspect the evaluator assumptions, circuit constructions, proofs, and resource accounting in the full paper. The modular-inversion construction is especially relevant to quantum cryptanalysis, while the DQI decoder provides a concrete example of trading a small permitted failure probability for a large reduction in logical resources.