Quantum low-density parity-check (qLDPC) codes are promising candidates for fault-tolerant quantum computation due to their high encoding rates and distances. However, implementing logical operations using qLDPC codes presents significant challenges. Previous research has demonstrated that self-dual qLDPC codes facilitate the implementation of transversal Clifford gates. Here we introduce a method for constructing self-dual qLDPC codes by stacking non-self-dual qLDPC codes. Leveraging this methodology, we develop double-chain bicycle codes, double-layer bivariate bicycle (BB) codes, double-layer twisted BB codes, and double-layer reflection codes, many of which exhibit favorable code parameters. Additionally, we conduct numerical calculations to assess the performance of these codes as quantum memory under the circuit-level noise model, revealing that the logical failure rate can be significantly reduced with high pseudo-thresholds.

翻译：量子低密度奇偶校验（qLDPC）码因其高编码率与距离，成为容错量子计算的有力候选方案。然而，利用qLDPC码实现逻辑操作面临重大挑战。先前研究已证明，自对偶qLDPC码有助于实现横向Clifford门。本文提出一种通过堆叠非自对偶qLDPC码来构造自对偶qLDPC码的方法。基于此方法，我们构建了双链自行车码、双层双变量自行车（BB）码、双层扭曲BB码以及双层反射码，其中多种码型展现出优异的码参数。此外，我们通过数值计算评估了这些码在电路级噪声模型下作为量子存储器的性能，结果表明其逻辑错误率可显著降低，并具有较高的伪阈值。