Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead through high-rate encodings, yet finite-size instances with practical logical error rates often achieve encoding rates only around or below $1/10$. Here, building on a recent ultra-high-rate construction by Kasai, we identify new structural conditions on the underlying affine permutation matrices that make encoding rates exceeding $1/2$ compatible with efficient implementation on reconfigurable neutral atom arrays. These conditions define a co-designed family of ultra-high-rate quantum codes that supports efficient syndrome extraction and atom rearrangement under realistic parallel control constraints. Using a hierarchical decoder with high accuracy and good throughput, we study the performance under a circuit-level noise model with $p=0.1\%$, achieving per-logical-per-round error rates of $1.3_{-0.9}^{+3.0} \times 10^{-13}$ with a $[[2304,1156,\leq 14]]$ code and $2.9_{-1.5}^{+3.1} \times 10^{-11}$ with a $[[1152,580,\leq 12]]$ code. These results approach the teraquop regime, highlighting the promise of this code family for practical ultra-high-rate quantum error correction.

翻译：量子纠错被广泛认为是大规模量子计算的关键技术，但所需的量子比特开销仍是核心挑战。量子低密度奇偶校验码通过高编码率可显著降低这一开销，然而在实际逻辑错误率下，有限尺寸实例的编码率通常仅接近或低于$1/10$。本文基于Kasai提出的超高速率构造方案，揭示了底层仿射置换矩阵的新结构条件，使得编码率超过$1/2$可与可重构中性原子阵列的高效实现兼容。这些条件定义了一个协同设计的超高速量子码族，在现实的并行控制约束下支持高效症候提取和原子重排。利用高精度、高吞吐的分层解码器，我们研究了电路级噪声模型（$p=0.1\%$）下的性能，使用$[[2304,1156,\leq 14]]$码实现了每逻辑轮次错误率$1.3_{-0.9}^{+3.0} \times 10^{-13}$，使用$[[1152,580,\leq 12]]$码实现了$2.9_{-1.5}^{+3.1} \times 10^{-11}$。这些结果接近Teraquop区域，凸显了该码族在实用超高速量子纠错中的前景。