AI 中文总结
该研究开发了统一图码与GKP码机制的因果框架，通过伴随子解析的Pauli框架译码实现基于测量的容错，经数值模拟确定了GKP晶格的伪阈值，为多种量子技术提供了统一控制层。
AI 中文摘要
图码为逻辑可观测量提供多个物理表征，而Gottesman-Kitaev-Preskill（GKP）码保留玻色位移噪声的模拟信息。我们开发了一个因果框架，在纯损耗后接量子限幅放大的场景下，将这些机制统一用于基于测量的容错。在该框架中，每个本地GKP恢复过程生成更新后的逻辑块、连续伴随子记录以及推断的Pauli类的置信分数。低置信度结果被刻意转换为定位擦除，因此可用性模式直接由玻色数据生成，而非独立采样。接受和拒绝的伴随子均对图分支的伴随子解析后验有贡献，该后验决定可访问的逻辑表征及输出的逻辑Pauli框架。我们推导了译码器条件分支限制、符号结果重构、Pauli框架更新、图-GKP模块的递归级联以及伴随子解析的逻辑融合。在多个压缩水平上的数值模拟确定了任务相关的容错行为，以及方形和六角GKP晶格的有限深度伪阈值。所得图-GKP接口为容错MBQC、基于融合的计算和全光子中继器提供了统一的因果控制层。
英文摘要
Graph codes offer multiple physical representatives of logical observables, while Gottesman-Kitaev-Preskill (GKP) codes retain analog information about bosonic displacement noise. We develop a causal framework that unifies these mechanisms for measurement-based loss tolerance under pure loss followed by quantum-limited amplification. In this framework, each local GKP recovery produces a refreshed logical block, a continuous syndrome record, and a confidence score for the inferred Pauli class. Low-confidence outcomes are deliberately converted into located erasures, so the availability pattern is generated directly from the bosonic data rather than sampled independently. Both accepted and rejected syndromes contribute to a syndrome-resolved posterior over the graph branch, which determines accessible logical representatives and the outgoing logical Pauli frame. We derive decoder-conditioned branch restriction, signed-outcome reconstruction, Pauli-frame updating, recursive concatenation of graph-GKP modules, and syndrome-resolved logical fusion. Numerical simulations across several squeezing levels identify task-dependent loss-tolerance behavior and finite-depth pseudothresholds for square and hexagonal GKP lattices. The resulting graph-GKP interface provides a unified causal control layer for fault-tolerant MBQC, fusion-based computation, and all-photonic repeaters.
