发表机构
Delft University of Technology（代尔夫特理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对qLDPC码错配提取电路，利用其Tanner图的边对称性，提出从底层组件而非完整量子码设计电路的方法，在提升积码、平衡积码和量子Tanner码上分别获得最优或近最优、深度最优的CNOT深度结果。
AI 中文摘要
量子低密度奇偶校验（qLDPC）码为可扩展的容错量子计算提供了有前景的途径，但其实际实现需要高效的错配提取电路。许多qLDPC码族通过显式构造由少量组件组装而成，这些构造在其Tanner图上印刻了边对称性。我们表明，可利用这些对称性从底层组件而非完整量子码设计错配提取电路。对于提升积码（Lifted Product codes）和平衡积码（Balanced Product codes），该方法可得到具有可证明最优或接近最优CNOT深度的解析构造；对于量子Tanner码，在我们测试的所有实例中均能生成深度最优电路，包括数据量子比特数近600的码。
英文摘要
Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computing, but their practical implementation requires efficient circuits for syndrome extraction. Many qLDPC families are assembled from a small set of components through explicit operations that imprint edge symmetries on their Tanner graphs. We show that disassembling the code by quotienting its symmetries one at a time, reduces parity-check circuit design to a much smaller problem acting only on the underlying components. Solutions to the reduced problem can then be lifted to the full code, yielding circuit constructions that apply to entire families of codes built from the same components. For lifted-product codes, our approach provides an optimal analytical construction for parity-check circuits achieving the lower bound on CNOT depth. We obtain analogous constructions for balanced-product codes and quantum--classical homological product codes. For quantum Tanner codes, the reduced problem is small enough to solve numerically, reaching the CNOT-depth lower bound for nearly all instance tested, including codes with up to 576 data qubits.
Comments20 pages, 5 figures, 2 Tables. Supplementary Material and GitHub updated
