Claude Mythos 5 beat the best published quantum circuits

Claude got a one-paragraph brief, worked for 53 hours, and was occasionally prompted "to think more broadly." That was nearly all the human input behind a new circuit for elliptic-curve point addition, one of eight quantum-circuit tasks where, according to Anthropic, Claude Mythos 5 beat the best published designs.

Andi Gu led the work as part of Anthropic's STEM Fellows Program. Alek Kemeny, a quantum physicist at Anthropic, was his mentor, and Susanne Yelin (Harvard University) and Mikhail Lukin (Harvard University and QuEra Computing) collaborated. The full paper is on arXiv. On October 15 we reported that applications for the next STEM Fellows cohort close on October 28, with the cohort starting in January 2027.

What the gains are measured against

The eight tasks are computational primitives, the basic routines that larger quantum algorithms are built from. They cover chemistry, optimization, quantum simulation, number theory and numerical computing. Anthropic says that on every one of them Claude's design used fewer qubits and fewer gates than the best previously published algorithm, in some cases by an order of magnitude or more. The one improvement the write-up states as a number is for a leading quantum optimization algorithm: Claude made its costliest step about 12x cheaper. For the other seven tasks the post shows the comparison in charts, and point addition gets a separate table.

Anthropic gives the size of the problem through FeMoco, the iron–sulfur cluster at the centre of nitrogenase, the enzyme bacteria use to turn atmospheric nitrogen 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 counting Toffolis is the standard way to estimate runtime. Later algorithmic work cut that estimate to about 340 million gates, roughly a 150,000-fold reduction (50 trillion divided by 340 million comes to about 147,000). At that count the computation would take a few hours on a future machine with about three million physical qubits. Anthropic notes that most of the savings came from redesigning circuits, not from better hardware.

That history matters when you read the claim. Human researchers have already found circuit-level gains running to five orders of magnitude. One of Claude's examples involves an iron-sulfide molecule, but the post does not set Claude's results against the 340-million FeMoco figure. It also doesn't say how much any of the eight primitives would shorten a complete application.

How the loop works

Claude writes each candidate circuit as a Python program. A separate evaluator checks that the circuit is correct and scores it, and the score goes back to Claude for the next attempt, with no human input between rounds. The score is the number of qubits multiplied by the number of gates, which Anthropic uses as a proxy for how long the circuit would take to run. Because a single number covers both, the objective rewards trading one resource against the other, not only cutting gates.

The setup depends on a property that not every quantum algorithm has. Anthropic targeted a fairly common class where each input produces one definite output that an ordinary computer can check, so the evaluator can confirm correctness without running quantum hardware. That requirement sets the real limit on where this method applies.

Anthropic says each improvement came from finding new structural or mathematical insight, not from fine-tuning existing designs. In the iron-sulfide circuit, Claude noticed that the molecule's symmetries and repeating structure meant some results could be computed once and reused, instead of being recomputed for each part of the system. In other tasks it found that published circuits included expensive components that were needed only for extremely rare inputs, and it redesigned the circuits without them.

The reversibility tax

Quantum circuits are hard to optimize for two reasons that ordinary code doesn't face. First, a circuit can't branch. It runs on a superposition of many inputs at once, and some inputs would take one path while others take the other, so the circuit has to include the operations for both every time. Second, it can't throw away scratch work. Every step must be reversible, and leftover intermediate data would corrupt the result. The only way to clear it is to "uncompute" it by running the steps that produced it in reverse, which costs extra gates.

This sets up a trade-off between space and time. If you uncompute intermediate results as soon as they've been used, you save qubits, but you pay in gates whenever a result has to be recomputed later. If you keep every result until the end, you avoid repeated work but may need many more qubits. A score of qubits times gates puts a price on exactly this trade-off.

Divsteps and point addition

Point addition combines two points on an elliptic curve to produce a third. It is the core step in quantum algorithms for the elliptic-curve discrete logarithm problem: given a starting point and the result of adding it to itself n times, find n. Those algorithms run point addition many times, including in reverse, and it accounts for most of their qubit and runtime costs. That is why it has become a standard benchmark. Anthropic asked Claude to work out how few qubits and how few gates it really needs, and told it to explore several approaches in parallel.

Most of the cost of point addition comes from modular inversion, the wraparound version of division: given a, find x such that ax ≡ 1 (mod p). Classical computers do this efficiently with a method called divsteps. It repeatedly simplifies a pair of numbers, and in each round it conditionally swaps, adds, subtracts or halves them. A classical program can discard the record of which operation it chose in each round. A quantum circuit has to keep that branch information so the computation can be run backward, and storing the full history in a direct quantum version takes an enormous number of extra qubits. Because of this, divsteps had never produced a practical quantum circuit.

Anthropic says Claude saw that divsteps could work for quantum circuits if there were some way to avoid storing the full history, and that its idea was that perhaps the record didn't need to be stored at all. The details of that construction are in the arXiv paper.

The model behind the results is not equally available to everyone. In its announcement on support for scientists, Anthropic says researchers in biology and chemistry are still limited to Opus-class models, and that it is working with the US government on an access program that would give life sciences professionals access to Mythos-class models.