AI 中文总结
本文提出Cornucopia码，一种硬件高效的量子低密度奇偶校验码，编码速率超1/2，伪阈值超0.4%，可大幅减少物理量子比特需求，实现超低开销量子纠错。
AI 中文摘要
抑制错误是实现有用的大规模量子计算的核心挑战。尽管量子纠错有望解决这一挑战，但现有量子纠错码通常在编码效率、错误阈值和硬件可行性之间存在权衡。本文介绍了Cornucopia码，这是一类实用、硬件高效的量子低密度奇偶校验码，在标准电路级噪声模型下，其编码速率超过1/2，同时保持伪阈值超过0.4%。受近期基于仿射置换的码构造方法以及可重构中性原子阵列中可用的长程连接性启发，本文采用结构化码几何，将码布局、原子重排和错码提取调度协同设计。该结构通过简单的并行原子重排实现非局域错码测量，完整的错码提取周期可并行测量所有X型和Z型校验，仅需12个纠缠层，与码块规模无关。所得阈值可与表面码和双变量自行车码相媲美。特别地，单个[[2844,1426,18]]码块可编码1426个距离为18的逻辑量子比特，假设物理错误率为0.1%（0.01%），外推得到每个逻辑量子比特每周期的逻辑错误率为2.6×10^-16（1.9×10^-31）。相比之下，双变量自行车码实现需超过68000个物理量子比特才能在可比逻辑错误率下编码相同数量的逻辑量子比特。这些结果使超低开销量子纠错的演示可在近期量子处理器上实现。
英文摘要
Suppressing errors is the central challenge for useful large-scale quantum computing. While quantum error correction promises a viable solution to this challenge, existing codes typically suffer from trade-offs among encoding efficiency, error threshold, and hardware feasibility. Here, we introduce Cornucopia codes, a family of practical, hardware-efficient quantum low-density parity-check codes that achieve an ultra-high encoding rate exceeding $1/2$ while maintaining a pseudo-threshold exceeding $0.4\%$ under the standard circuit-level noise model. Inspired by recent affine-permutation-based code constructions and the long-range connectivity available in reconfigurable neutral-atom arrays, we adopt a structured code geometry in which the code layout, atom rearrangement, and syndrome-extraction schedule are co-designed. This structure enables nonlocal syndrome measurements through simple, parallel atom rearrangements. A complete syndrome extraction cycle measures all $X$- and $Z$-type checks in parallel with $12$ entangling layers, independent of the code size. The resulting threshold is comparable to those of the surface code and bivariate bicycle codes. In particular, a single code block $[[2844,1426,18]]$ encodes $1{,}426$ distance-$18$ logical qubits, achieving an extrapolated logical error rate of $2.6\times10^{-16}$ ($1.9\times10^{-31}$) per logical qubit per cycle, assuming the physical error rate of $0.1\%$ ($0.01\%$). By comparison, a bivariate bicycle code implementation would require more than $68{,}000$ physical qubits to encode the same number of logical qubits at a comparable logical error rate. These results bring demonstrations of ultra-low-overhead quantum error correction within the reach of near-term quantum processors.
