Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, potentially enabling low-overhead fault-tolerant quantum computing. However, implementing qLDPC codes involves nonlocal operations that require long-range connectivity between qubits. This makes their physical realization challenging in comparison to geometrically local codes, such as the surface code. Here we propose a hardware-efficient scheme for fault-tolerant quantum computation with high-rate qLDPC codes that is compatible with the recently demonstrated capabilities of reconfigurable atom arrays. Our approach utilizes the product structure inherent in many qLDPC codes to implement the nonlocal syndrome extraction circuit through atom rearrangement, resulting in an effectively constant overhead. We prove the fault tolerance of these protocols, and our simulations show that the qLDPC-based architecture starts to outperform the surface code with as few as several hundred physical qubits. We further find that quantum algorithms involving thousands of logical qubits can be performed using less than 10⁵ physical qubits. Our work suggests that low-overhead quantum computing with qLDPC codes is within reach using current experimental technologies.

量子低密度奇偶校验（qLDPC）码可以实现高编码率和良好的码距缩放，从而有可能实现低开销的容错量子计算。然而，实现 qLDPC 码涉及非局部操作，需要量子位之间的远程连接。与几何局部代码（例如表面代码）相比，这使得它们的物理实现具有挑战性。在这里，我们提出了一种使用高速 qLDPC 代码进行容错量子计算的硬件高效方案，该方案与最近展示的可重构原子阵列的功能兼容。我们的方法利用许多 qLDPC 码固有的乘积结构，通过原子重排来实现非局部校正子提取电路，从而产生有效的恒定开销。我们证明了这些协议的容错能力，并且我们的模拟表明，基于 qLDPC 的架构开始优于仅具有数百个物理量子位的表面代码。我们进一步发现涉及数千个逻辑量子位的量子算法可以使用少于 10 ^{5 个}物理量子位来执行。我们的工作表明，使用当前的实验技术可以实现使用 qLDPC 码的低开销量子计算。