Designing more efficient quantum circuits with Claude

Claude Mythos 5 discovered new quantum circuit designs for eight computational primitives that outperform previously published state-of-the-art solutions in both qubit and gate counts. In some cases, the performance improvement exceeded an order of magnitude, suggesting AI can accelerate the timeline for practical quantum computing.

Methodology and Approach

The study used Claude Mythos 5 in a closed-loop system with natural language specifications and automated evaluators. The model optimized for accuracy first, then scored designs based on the product of qubit count and gate count. Unlike human researchers who often refine existing designs, Claude identified structural and mathematical insights, such as leveraging molecular symmetry or removing unnecessary high-cost components for rare inputs.

Elliptic Curve Point Addition

For the modular inversion step in elliptic curve point addition, Claude proposed a reversible implementation of divsteps that does not store branch history. Instead, it decodes branch information by inspecting number pairs after iteration. This approach, formally verified in Lean, resulted in a design with 12% more qubits but a 17x reduction in gate count compared to the previous minimum-qubit design.

Decoded Quantum Interferometry (DQI)

Claude optimized the Reed-Solomon decoder, the most expensive step in DQI algorithms for optimization problems. By switching from the Extended Euclidean Algorithm to Berlekamp-Massey decoding, which fits the fixed gate sequence constraints of quantum circuits, Claude reduced the gate count by 12x. Further memory optimizations allowed the design to use only 19 qubits for storage in nearly all cases, a significant reduction compared to the 840 qubits required by a naive reversible version of the Berlekamp-Massey approach.

Implications

While historical reductions in quantum resource estimates, such as the 150,000x decrease for FeMoco ground-state energy calculations, took eight years of human research, Claude’s elliptic-curve design was the result of a single 53-hour run. The findings indicate that AI can jointly optimize algorithmic and hardware components, potentially enabling fault-tolerant quantum computers to solve problems in catalysis and materials science sooner.