Quantum computing is deemed to require error correction at scale to mitigate physical noise by reducing it to lower noise levels while operating on encoded logical qubits. Popular quantum error correction schemes include CSS code, of which surface codes provide regular mappings onto 2D planes suitable for contemporary quantum devices together with known transversal logical gates. Recently, qLDPC codes have been proposed as a means to provide denser encoding with the class of bivariate bicycle (BB) codes promising feasible design for devices. This work contributes a novel subclass of BB codes suitable for quantum error correction. This subclass employs {\em coprimes} and the product $xy$ of the two generating variables $x$ and $y$ to construct polynomials, rather than using $x$ and $y$ separately as in vanilla BB codes. In contrast to vanilla BB codes, where parameters remain unknown prior to code discovery, the rate of the proposed code can be determined beforehand by specifying a factor polynomial as an input to the numerical search algorithm. Using this coprime-BB construction, we found a number of surprisingly short to medium-length codes that were previously unknown. We also propose a layout on cold atom arrays tailored for coprime-BB codes. The proposed layout reduces both move time for short to medium-length codes and the number of moves of atoms to perform syndrome extractions. We consider an error model with global laser noise on cold atoms, and simulations show that our proposed layout achieves significant improvements over prior work across the simulated codes.

翻译：量子计算被认为需要大规模纠错，通过在编码的逻辑量子比特上操作，将物理噪声降低至较低水平。主流量子纠错方案包括CSS码，其中表面码提供了规则映射到二维平面的方法，适用于当代量子设备，并具备已知的横向逻辑门。最近，qLDPC码被提出作为一种提供更密集编码的手段，其中二元自行车（BB）码类有望为设备提供可行的设计。本工作贡献了一类适用于量子纠错的新型BB码子类。该子类采用{\em 互质数}以及两个生成变量$x$和$y$的乘积$xy$来构造多项式，而非像普通BB码那样分别使用$x$和$y$。与普通BB码在码发现前参数未知不同，所提出码的码率可以通过指定一个因子多项式作为数值搜索算法的输入而预先确定。利用这种互质-BB构造，我们发现了一些先前未知的、长度出奇短至中等的码。我们还提出了一种专为互质-BB码设计的冷原子阵列布局。所提出的布局减少了中短码的移动时间以及执行综合征提取所需的原子移动次数。我们考虑了一个包含冷原子上全局激光噪声的误差模型，仿真结果表明，在所仿真的码中，我们提出的布局相比先前工作取得了显著改进。