中等码长下的量子Tanner码
Quantum Tanner Codes at Moderate Blocklength
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中文总结 AI 辅助
该研究通过两种互补方法构造中等码长的量子Tanner码，得到多个距离上界超20的新码实例，其伪阈值与短码长结果相当，还提供了相关开源Julia库。
中文摘要 AI 辅助
我们通过两种互补方法给出了具有良好码率和距离的量子Tanner（QT）码的显式构造：左右Cayley复形（LRCC）描述和“提升”视角，其中通过有限群𝒢的左右正则交换作用，将种子Calderbank-Shor-Steane（CSS）码进行提升。通过对GAP的SmallGrp库中非阿贝尔群的广泛搜索，我们研究了中等码长范围（n∈[500,1000]），并识别出多个距离上界超过20的新码实例，包括[[480,8,(≤21,≤21)]]、[[504,4,(≤36,≤27)]]、[[672,4,(≤48,≤28)]]、[[720,6,(≤30,≤30)]]和[[864,8,(≤39,≤31)]]，这些上界是通过最多3.5亿次sQetch（一种随机距离估计器）试验获得的。所提出的码实例的校验权重范围为9至20。使用Tesseract解码器，我们估计在现象学噪声下伪阈值为3.6%–4.6%，在电路级噪声下为0.14%–0.27%，与较短码长下的先前结果相当。我们还提供了该httpURL，这是一个用于构造QT码和Ramanujan图显式构造的开源Julia库。
英文摘要
We present explicit constructions of quantum Tanner (QT) codes with good rate and distance, obtained through two complementary approaches: the left-right Cayley complex (LRCC) description and the "lifting" perspective, in which a seed Calderbank-Shor-Steane (CSS) code is lifted by commuting left-right regular actions of a finite group $\mathcal{G}$. Through an extensive search over non-abelian groups from GAP's SmallGrp library, we investigate the moderate-blocklength regime ($n \in [500,1000]$) and identify several new code instances with distance upper bounds exceeding $20$. These include $[[480,8,(\leq 21,\leq 21)]]$, $[[504,4,(\leq 36,\leq 27)]]$, $[[672,4,(\leq 48,\leq 28)]]$, $[[720,6,(\leq 30,\leq 30)]]$, and $[[864,8,(\leq 39,\leq 31)]]$, with these bounds obtained using up to $350$ million trials of sQetch, a randomized distance estimator. The code instances presented have check weights ranging from $9$ to $20$. Using the Tesseract decoder, we estimate pseudo-thresholds of $3.6\%$-$4.6\%$ under phenomenological noise and $0.14\%$-$0.27\%$ under circuit-level noise, comparable to prior results at shorter code lengths. We also provide QuantumExpanders$.$jl, an open-source Julia library for constructing QT codes and explicit constructions of Ramanujan graphs.
