Quantum

Geometry-optimized hyperbolic codes for modular fault-tolerant quantum architectures

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Briefings

This article presents finite families of hyperbolic surface codes that achieve optimal efficiency scaling $kd^2/n = C (\log{k})^2$ for modular fault-tolerant architectures. By optimizing periodic identifications, the code distance is doubled, increasing efficiency by a factor of four at fixed qubit counts. A topology-aware algorithm partitions hyperbolic codes into bounded planar modules to reduce long-range communications. Circuit-level Monte Carlo simulations indicate that tripling the long-range gate error probability slightly lowers but does not eliminate the estimated error-correction thresholds, strengthening the case for these structured codes in future architectures.

Key points

• The study introduces finite families of hyperbolic surface codes leveraging optimal efficiency scaling $kd^2/n = C (\log{k})^2$ attainable by surface codes with bounded local geometry.
• Optimizing periodic identifications in these codes doubles the code distance, increasing efficiency by a factor of four at fixed qubit counts, encoding rate, and parity-check weight.

Context and limitations

Circuit-level Monte Carlo simulations provide finite-size threshold estimates for both modular and monolithic layouts, but tripling the long-range gate error probability only mildly lowers the estimated error-correction thresholds, leaving uncertainty regarding exact fault-tolerance boundaries.

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