Generalized Z_p toric codes as qudit low-density parity-check codes

Zijian Liang, Yu-An Chen · 2026 · arXiv

| 编号 QE034 | 主题 基础理论 | 链接 arXiv:2602.20158 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

We study two-dimensional translation-invariant CSS stabilizer codes over prime-dimensional qudits on the square lattice under twisted boundary conditions, generalizing the Kitaev ${\mathbb{Z}}_p$ toric code by augmenting each stabilizer with two additional qudits. Using the Laurent-polynomial formalism, we adapt the Gr¨obner basis to compute the logical dimension k eficiently, without explicitly con structing large parity-check matrices. We then perform a systematic search over various stabilizer realizations and lattice geometries for $p\in 3,5,7,11$ , identifying qudit low-density parity-check codes with the optimal finite-size performance. Representative examples include [[242, 10, 22]] 3 and $[[120,6,20]{]}_{11}$ , both achieving $k{d}^2/n=20$ . Across the searched regime, the best observed $\ddot{k}{d}^2$ at fixed n increases with $p,$ with an empirical relation $k{d}^2=0.0541n^2\ln p+3.84n,$ compatible with a Bravyi–Poulin–Terhal–type tradeof when the interaction range grows with system size.

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