Anthropic’s Claude Mythos 5 has developed a quantum circuit design that uses 17 times fewer gates than a previous approach. The result could help engineers run sophisticated quantum algorithms with fewer computing resources. It also offers a new way to address one of the biggest technical challenges of quantum computing: balancing memory requirements and processing time.
The design emerged from a 53-hour experiment led by researcher Andi Gu as part of Anthropic’s STEM Fellows program. Claude developed a reversible arithmetic algorithm for computing elliptic curves, with researchers from Harvard University and QuEra Computing collaborating on the work. The results suggest that automated circuit design could accelerate progress toward practical quantum computers.
Rethinking quantum circuit design
Quantum computers process information using qubits, which can represent combinations of states through superposition. However, existing machines only have hundreds to thousands of qubits, and environmental interference can lead to errors in the calculation.
Engineers therefore need to make quantum circuits as efficient as possible. Each operation consumes computing resources, while storing intermediate results requires additional qubits. Quantum circuits also cannot simply discard temporary information because their operations must remain reversible.
Anthropic commissioned Claude to optimize eight computing modules in the areas of chemistry, physics simulation, optimization, number theory and numerical computing. An automated evaluator reviewed each design for accuracy and assessed its resource requirements.
Claude Mythos 5 went through repeated design and testing cycles, refining his proposals without human intervention between rounds. The results improved over previously published designs, with some reductions reaching an order of magnitude or greater.
Solve a storage problem
A particularly notable result concerns modular inversion, a mathematical operation used in elliptic curve arithmetic. The operation plays a central role in quantum algorithms targeting the discrete logarithm problem with elliptic curves.
Claude focused on an algorithm called divsteps, which simplifies numerical values through repeated conditional operations. Classical computers can perform this method efficiently, but implementing it in quantum circuits creates a major memory problem.
A reversible circuit must preserve enough information to reconstruct each computational step. Divsteps therefore requires a record of its branching decisions, potentially consuming an enormous number of additional qubits.
Claude developed a way to recover these decisions directly from intermediate numerical values. To establish the method, mathematical identities were derived, the approach was tested through numerical simulations, and its correctness was formalized using Lean.
The resulting circuit eliminates the need to store the complete history of branch decisions. Claude then explored hybrid designs that store some information and reconstruct the rest.
One design uses 12 percent more qubits than the smallest previous design but requires 17 times fewer gates. This compromise expands the options available to engineers working with limited quantum hardware.
Shortening the timeline for quantum computing
Anthropic also reported improvements in its other circuit design tasks. An optimization reduced the most costly step of a leading quantum optimization algorithm by about 12 times.
The findings follow years of progress in reducing the resources required for useful quantum calculations. Researchers estimated in 2017 that simulating the ground-state energy of FeMoco, an iron-sulfur cluster involved in biological nitrogen fixation, would require about 50 trillion Toffoli gates.
Later advances reduced this estimate to about 340 million gates, a reduction of about 150,000 times. Anthropic argues that automated circuit optimization could help accelerate similar advances.
Important obstacles remain. Quantum computers continue to require better error correction, reliable hardware controls, and systems that can manage fragile qubits during longer calculations. Still, AI-designed circuits could help researchers use future machines more efficiently.
