AI 中文总结
该研究构建了颜色码的逻辑编译框架，利用其拓扑结构与 ZX 图的对应关系开发自动化编译策略，实现了逻辑计算到颜色码时空布局的转换，推进了颜色码架构向全栈量子计算发展。
AI 中文摘要
容错量子计算需要对逻辑 primitive 进行系统级协调。本文基于颜色码的拓扑结构，构建了支持通用逻辑操作的逻辑编译框架。利用其任意子凝聚和畴壁结构，引入了捕捉逻辑块与操作的时空框图表示，并推导了块组装规则。与 ZX 图的对应关系进一步明确了该表示的逻辑语义，实现了保持所表示计算的变换。此外，开发了代码衍生的编译策略，将逻辑计算的 ZX 表示转换为有效的颜色码时空布局：带边装饰的 ZX 图在块组装约束下适配颜色码的逻辑表示，融合区域感知路由在几何嵌入中利用语义等价性。本文实现了完整逻辑编译流程的自动化，在广泛的算法上演示了成功编译。本研究推动颜色码架构从单个原语向逻辑计算的自动化合成发展，是实现全栈量子计算的重要一步。
英文摘要
Fault-tolerant quantum computing requires system-level coordination of logical primitives. Here, we establish a logical compilation framework for the color code, grounded in its topological structure and supporting universal logical operations. Based on its anyon-condensation and domain-wall structure, we introduce a spacetime block-diagram representation capturing logical patches and operations and derive the rules governing block assembly. A correspondence with ZX diagrams further identifies the logical semantics of this representation and enables transformations that preserve the represented computation. Moreover, we develop a code-derived compilation strategy that converts ZX representations of logical computations into valid color-code spacetime layouts. In this strategy, edge-decorated ZX diagrams tailor the logical representation to the color code under the block-assembly constraints, and fusion-region-aware routing exploits semantic equivalence during geometric embedding. We automate the complete logical compilation process and demonstrate successful compilation across a broad range of algorithms. Our work advances color-code architecture from individual primitives to the automated synthesis of logical computations, marking a significant step toward its full-stack quantum computing.
