Independent Trivariate Bicycle Codes

Aygul Azatovna Galimova · 2026 · arXiv 2026

| 编号 QE149 | 主题 qLDPC 码 | 链接 arXiv:2603.17703 |

摘要

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We introduce six independent trivariate bicycle (ITB) codes, which extend the bivariate bicycle framework of Bravyi et al.\ to three cyclic dimensions. Using asymmetric polynomial pairs on three-dimensional tori, we construct four codes including a $[[140,6,14]]$ code with $k{d}^2/n=8.40$. In the code-capacity setting, the $[[140,6,14]]$ code achieves a pseudothreshold of $8.0$ and $k{d}^2/n=8.40$, exceeding the best multivariate bicycle code of Voss et al.\ ($7.9$, $k{d}^2/n=2.67$). With circuit-level depolarizing noise, pseudothresholds reach $0.59$ for $[[140,6,14]]$ and $0.53$ for $[[84,6,10]]$. On the SI1000 superconducting noise model, the $[[140,6,14]]$ code achieves a per-rou

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