Generalized $\mathbb{Z}_p$ toric codes as qudit low-density parity-check codes
Zijian Liang Yu-An Chen
作者信息
Abstract
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 Gröbner basis to compute the logical dimension $k$ efficiently, without explicitly constructing 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 $k d^{2}$ at fixed $n$ increases with $p$, with an empirical relation $k d^{2} = 0.0541 \, n^{2}\ln p + 3.84 \, n$, compatible with a Bravyi--Poulin--Terhal-type tradeoff when the interaction range grows with system size.引用本文复制引用
Zijian Liang,Yu-An Chen.Generalized $\mathbb{Z}_p$ toric codes as qudit low-density parity-check codes[EB/OL].(2026-02-23)[2026-02-25].https://arxiv.org/abs/2602.20158.学科分类
物理学
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