常数穿梭深度的qLDPC码并行代数手术

中文摘要 AI 辅助

可重构原子阵列为实现高码率的量子低密度奇偶校验码提供了一个有前景的平台，但其计算优势取决于能否在不产生高昂穿梭和空间开销的情况下实现逻辑操作。我们针对提升积码引入了代数手术，共同设计逻辑测量、辅助码和原子穿梭，以实现硬件高效的泡利乘积测量。这些协议在循环对称约束下提供了灵活的逻辑可寻址性，支持广泛的并行逻辑测量类别，包括物理支撑高度重叠的典型逻辑算子和代码块内或代码块间（即使具有不同提升尺寸）的联合测量，同时在明确布局假设下在中性原子处理器上实现常数穿梭深度。在一个代表性硬件模型基准测试中，支持33个并行典型逻辑测量的周期比所比较的基于单一可观测量的图手术调度快约2倍，且量子比特开销具有竞争力。这些穿梭和电路级模拟证实，量子低密度奇偶校验码的代数结构不仅可用于降低空间开销，还可简化物理实现并扩展中性原子处理器上可高效访问的逻辑操作集合。

英文摘要

Reconfigurable atom arrays provide a promising platform for high-rate quantum low-density parity-check codes, but their computational advantage depends on whether logical operations can be implemented without incurring prohibitive shuttling and space overheads. We introduce algebraic surgery for lifted product codes, co-designing the logical measurements, auxiliary codes, and atom shuttling to enable hardware-efficient Pauli-product measurements. These protocols provide flexible logical addressability subject to the cyclic-symmetry constraint, enabling a broad class of parallel logical measurements, including canonical logical operators with heavily overlapping physical supports and joint measurements within or between code blocks even with different lift sizes, while achieving constant shuttling depth on neutral-atom processors under explicit layout assumptions. In a representative hardware-model benchmark, a cycle supporting 33 parallel canonical logical measurements is about $2\times$ faster than the compared single-observable graph-based surgery schedules, with competitive qubit overhead. These shuttling and circuit-level simulations confirm that the algebraic structure of quantum low-density parity-check codes can be used not only to reduce space overhead, but also to simplify physical implementation and expand the set of efficiently accessible logical operations on neutral-atom processors.

发表机构

• University of Geneva（日内瓦大学）
• Freie Universität Berlin（柏林自由大学）
• Eastern Institute of Technology（东方理工大学）

机构由 AI 辅助整理，请以论文原文为准。