标题： 通过时空级联的容错协议 显示英文标题

标题： Fault-tolerant protocols through spacetime concatenation

摘要： 我们引入了一个称为时空连接的框架，用于容错编译稳定子码的奇偶校验提取电路。 时空连接通过结构化的装置布局和编码矩阵，使奇偶校验提取电路能够高效地编译为动态码，从而实现低权重测量同时保持逻辑信息。 我们的框架使用了足以保证动态码容错性的条件，包括不测量逻辑算符和保持时空距离。 我们利用该框架构建了动态码的显式示例，包括动态双变量自行车码和一个动态Haah码，并展示了它们的容错特性。 此外，我们分析了动态码的分类和资源权衡，证明了它们对硬件约束的适应性，包括制造缺陷和量子比特丢失的情况。 显示英文摘要

摘要： We introduce a framework called spacetime concatenation for fault-tolerant compilation of syndrome extraction circuits of stabilizer codes. Spacetime concatenation enables efficient compilation of syndrome extraction circuits into dynamical codes through structured gadget layouts and encoding matrices, facilitating low-weight measurements while preserving logical information. Our framework uses conditions that are sufficient for fault-tolerance of the dynamical code, including not measuring logical operators and preserving the spacetime distance. We construct explicit examples of dynamical codes using this framework, including the dynamical bivariate bicycle code and a dynamical Haah code, while illustrating their fault-tolerant properties. Furthermore, we analyze the classification and resource trade-offs of dynamical codes, demonstrating their adaptability to hardware constraints, including fabrication defects and qubit dropout scenarios.