Anthropic says Claude beat published quantum circuit designs across eight tasks

Key Points

1. Anthropic says Claude redesigned eight quantum circuits, beating the best published designs on both qubits and gates.
2. Quantum machines today hold only hundreds to thousands of noisy qubits, far short of practical algorithms.
3. Cheaper circuits cut the hardware needed, which Anthropic says could pull useful quantum computing forward in time.

The latest:

Claude produced quantum circuit designs that use fewer qubits and fewer gates than the best previously published versions across eight computational primitives, Anthropic said, with gains reaching an order of magnitude or more in some cases. The work covered chemistry, optimization, physics simulation, number theory and numerical computing. Anthropic said the model worked largely on its own, guided by an automated scoring program.

Details:

• The setup: Anthropic said it handed Claude plain-language specifications for eight circuits plus an automated evaluator that checked each design for correctness and scored it on qubits multiplied by gates, a proxy for runtime. Claude wrote the circuits as Python programs and revised in a closed loop with no human input between rounds.
• Who ran it: The project was led by Andi Gu through Anthropic’s STEM Fellows Program, mentored by Anthropic quantum physicist Alek Kemeny, with Susanne Yelin of Harvard University and Mikhail Lukin of Harvard University and QuEra Computing. Anthropic said the full paper is posted on arXiv. The model used was Claude Mythos 5.
• The constraint: Quantum circuits cannot branch like ordinary code and cannot discard scratch work, because every step must be reversible. Leftover intermediate data corrupts the result, so it must be uncomputed by running the calculation backward, at the cost of extra gates. Both constraints make quantum circuits far costlier than classical equivalents.
• Modular inversion: The first task was point addition on elliptic curves, a standard field benchmark. Anthropic said Claude worked 53 hours with minimal human input before reaching a new approach to modular inversion, the step that dominates the cost. A quantum version of the classical divsteps method normally stores a long branch history, demanding enormous extra qubits.
• How it worked: Claude proposed inferring the branch record directly from the number pairs after each iteration instead of storing it. Early candidate rules worked on small cases but failed at the full 256-bit size. Anthropic said the model then proved several new algebraic identities, derived a precise decoding formula, validated it in large-scale numerical simulations, and formalized the claim in Lean.
• The trade-off: Decoding saves qubits but costs time, so Claude varied the threshold at which the circuit stores rather than decodes branch information, producing a family of designs. Against the smallest previous design, one variant uses 12% more qubits but 17 times fewer gates. Anthropic said the designs expand the Pareto frontier of qubit-runtime combinations.
• The optimizer: The second showcased result cut the costliest step of decoded quantum interferometry, an optimization algorithm Anthropic described as one of the strongest candidates for a superpolynomial speedup, by about 12 times. That step is an error-correcting decoder; the original demonstration used a Reed-Solomon decoder on a grid-based curve-fitting problem called optimal polynomial intersection.
• The chemistry benchmark: Anthropic cited FeMoco, the iron-sulfur cluster in nitrogenase, where 2017 estimates put the cost of computing ground-state energy at roughly 50 trillion Toffoli gates. Successive algorithmic advances brought that to about 340 million, a roughly 150,000-fold cut, equal to a few hours on a future machine with about 3 million physical qubits.
• The method: Anthropic said the gains came from new structural and mathematical insights rather than tuning existing designs. In one iron-sulfide simulation, Claude exploited the molecule’s symmetries and repeating structure to compute some results once and reuse them. Elsewhere it stripped out costly components that existing circuits carried only to handle extremely rare inputs.

Background:

Quantum computers store information in qubits built from atoms, superconducting circuits or light particles, which can hold multiple states at once. Existing machines have only hundreds to thousands of qubits and are highly sensitive to heat, vibration and cosmic rays, with small errors accumulating until the output is wrong.

Between the lines:

The FeMoco figures frame Anthropic’s core argument: most of the 150,000-fold cost reduction in that benchmark came from redesigning circuits, not from better hardware. If circuit design is the bottleneck and a model can iterate against an automated correctness checker for days without supervision, the timeline to useful quantum applications becomes partly a software problem. The decoder gains shown here remain confined to the eight primitives tested.

What’s next

The arXiv paper is the next place the decoding formula and the point-addition resource counts can be checked against the published designs from Schrottenloher and Luo et al. that Anthropic benchmarked against.