Claude cut a quantum circuit's gate count 17x in 53 hours

Before Claude settled on 19 qubits of scratch memory for a quantum decoder, it wrote its own high-speed simulator and ran 403 million sample decodings to see how often it would need more. Reserving room for the worst case would have taken 665 qubits. According to Anthropic's write-up of the project, this habit of measuring what a circuit actually needs, together with finding mathematical structure that published designs missed, is how Claude Mythos 5 beat the best published designs for eight quantum circuits.

Andi Gu led the work as part of Anthropic's STEM Fellows Program. Alek Kemeny, a quantum physicist at Anthropic, mentored it, and Susanne Yelin (Harvard University) and Mikhail Lukin (Harvard University and QuEra Computing) collaborated. The full paper is on arXiv. All eight tasks are computational primitives, the routines that larger quantum algorithms are built from. They cover chemistry, optimization, quantum simulation, number theory and numerical computing. Anthropic says Claude's designs beat the previous best on both qubits and gates, in some cases by an order of magnitude or more.

Why circuits matter

Today's quantum computers have hundreds to thousands of noisy qubits. For years the field has cut costs mostly by redesigning circuits, with little of the gain coming from better hardware. Anthropic's example is FeMoco, the iron–sulfur cluster at the heart of nitrogenase, the enzyme bacteria use to turn nitrogen from the air into ammonia. In 2017, researchers estimated that computing FeMoco's ground-state energy would take about 50 trillion Toffoli gates. The Toffoli is one of the most expensive gates to run, so the field counts them to estimate runtime. Through a series of algorithmic advances, that estimate has fallen to about 340 million gates. That is roughly a 150,000-fold reduction, or a few hours on a future machine with about three million physical qubits. Anthropic says the drop took many research groups eight years, and each step typically took months.

The benchmark has a complication of its own. As Quantum Frontiers reports, a 2026 preprint by Zhai et al. presents a classical solution of the FeMo-cofactor model to chemical accuracy. Its authors published a commentary on March 12 about what the result means for quantum computing.

A loop with a scorer

The setup is simple. Claude writes a circuit design in Python and sends it to an automated evaluator. The evaluator checks that the design is correct and scores it by multiplying the number of qubits by the number of gates, which stands in for runtime. Claude gets the score back and tries again, with no human input between rounds.

Anthropic says three things made the task a good fit. Circuits can be written as ordinary code. The class of algorithms it targeted can be checked efficiently, because each input produces one definite output that a classical computer can verify. And the score is objective. According to Anthropic, every improvement came from new structural or mathematical insight, not from fine-tuning existing designs. In one circuit for simulating an iron-sulfide molecule, Claude noticed that the molecule's symmetries and repeating structure let some results be calculated once and reused. In other cases, it found costly components that existing circuits needed only for extremely rare inputs, and it redesigned the circuits without them.

Reading the 17x

The task that drew the headline is elliptic-curve point addition, the rule for combining two points on an elliptic curve into a third. It is the core step of quantum algorithms for the elliptic-curve discrete logarithm problem, and it has become one of the field's standard benchmarks. Claude got a one-paragraph brief that explained the math and the evaluator and told it to explore several approaches in parallel. It worked for 53 hours with minimal human input, limited to that brief and occasional prompts to think more broadly.

The best-known result is a trade-off rather than a win on both counts. Compared with the smallest previous design, one of Claude's circuits uses 12% more qubits and 17x fewer gates. On the evaluator's own metric, that works out to roughly a 15x improvement (17 divided by 1.12). This circuit is one of a family of designs that Anthropic says expands the Pareto frontier: they offer combinations of qubit count and runtime that weren't available before. The comparison designs come from Schrottenloher (2026) and Luo et al. (2026).

Divsteps without a record

Most of the cost of point addition comes from modular inversion, which is division in arithmetic that wraps around at a fixed limit: given a, find x such that ax ≡ 1 (mod p). Classical computers do this efficiently with divsteps. The method takes a pair of numbers and, over many rounds, conditionally swaps, adds, subtracts or halves them.

Two quantum constraints have kept divsteps from producing a practical circuit. A quantum circuit can't branch, because it runs on a superposition of inputs and must include the operations for every path. It also can't discard scratch work. Every step must be reversible, and any leftover intermediate data corrupts the result unless it is uncomputed by running the steps that produced it in reverse. So a straightforward quantum divsteps has to keep the branch information, a record of which operation ran in each round, and that takes an enormous number of extra qubits.

Claude's idea was to skip storing the record and decode the branch choice from the pair of numbers after each round. In effect, the numbers would carry their own history, the way footprints in snow let you retrace a route without a logbook. Its first simple decoding rules worked on small cases but failed at the full 256-bit size. Claude then took a more theoretical route. It proved a series of results about the iteration, including several new algebraic identities, and derived an exact decoding formula from them. It checked the formula with large-scale numerical simulations, then formalized the claim in Lean. Anthropic calls the result the first reversible implementation of divsteps with no stored branch history.

Decoding saves qubits but costs time. The family of designs comes from varying the threshold at which the circuit stores branch information rather than decoding it.

A decoder sized by sampling

The second result concerns decoded quantum interferometry (DQI), which Anthropic calls one of the strongest candidates for a superpolynomial quantum speedup on optimization problems. DQI prepares a state in which good solutions are more likely to be read out. To do that it relies on an error-correcting decoder, which is the algorithm's most expensive step. On optimal polynomial intersection (OPI), a grid-based form of curve fitting, that decoder is a Reed–Solomon decoder. Estimates by researchers at Google Quantum AI imply that one OPI problem would take about three months on the Frontier supercomputer and roughly an hour on a future quantum computer running DQI. Most of that hour would go to Reed–Solomon decoding.

The previous design (Khattar et al., 2025) used the extended Euclidean algorithm, whose number and order of steps depend on the input. A fixed quantum circuit therefore had to run more rounds than any single input needed and execute every operation in every round. Claude switched to Berlekamp–Massey decoding, which reads the syndromes one at a time, performs the same kind of step every round and always runs the same number of rounds.

A naive reversible Berlekamp–Massey stores a 12-qubit record every round, which adds up to 840 qubits. Claude's version reconstructs most of that history from the updated state, using the same move as with divsteps. A few exceptional values still have to be saved. Allowing for exceptions in 35 rounds would cost 665 qubits, so Claude ran the 403 million samples, found that almost every run needed to save one value at most, and reserved 19 qubits. About one run in 10,000 needs more and fails, which is within the error rate the task allows. Altogether, the decoder uses 12 times fewer gates than Google's previous construction.

Where humans stepped in

Anthropic describes the limits plainly. In early experiments Claude was conservative. It second-guessed apparent improvements, double- and even triple-checked results that were already well supported, and leaned toward well-known approaches over new ones. The same caution is what led it to write the Lean proofs for divsteps, and over-checking is the cheaper flaw when it produces a proof. The team responded by requiring several qualitatively different approaches developed in parallel, and by occasionally prompting Claude to broaden its search. Once Claude had the divsteps idea, Anthropic says, it developed, implemented and verified the approach on its own. On September 28 we wrote about a similar question of credit: Claude's enzyme discovery began with five examples supplied by scientists.

Anthropic's next goal is larger than single circuits. Error-correcting codes, fast decoders and hardware control share the traits that made circuits a good fit: each can be written as code, checked and scored. Anthropic writes:

Rather than designing each component on its own, AI could optimize all of them jointly, from the algorithm down to the hardware, to build an entire error-corrected quantum computer tailored to a specific problem.