Source code and data underlying the publication "Fault-tolerant modular quantum computing with surface codes using single-shot emission-based hardware"

Fault-tolerant modular quantum computing requires stabilizer measurements across the modules in a quantum network. For this, entangled states of high quality and rate must be distributed. Currently, two main types of entanglement distribution protocols exist, namely emission-based and scattering-based, each with its own advantages and drawbacks. On the one hand, scattering-based protocols with cavities or waveguides are fast but demand stringent hardware such as high-efficiency integrated circulators or strong waveguide coupling. On the other hand, emission-based platforms are experimentally feasible but so far rely on Bell-pair fusion with extensive use of slow two-qubit memory gates, limiting thresholds to ~0.16%. Here, we consider a fully distributed surface code using emission-based entanglement schemes that generate GHZ states in a single shot, i.e., without the need for Bell-pair fusions. We show that our optical setup produces Bell pairs, W states, and GHZ states, enabling both memory-based and optical protocols for distilling high-fidelity GHZ states with significantly improved success rates. Furthermore, we introduce protocols that completely eliminate the need for memory-based two-qubit gates, achieving thresholds of ~0.19% with modest hardware enhancements, increasing to above ~0.24% with photon-number-resolving detectors. These results show the feasibility of emission-based architectures for scalable fault-tolerant operation.容错模块化量子计算需要在量子网络的各模块间开展稳定子测量（stabilizer measurements）。为此，需分发高质量且高产生速率的纠缠态（entangled states）。当前主流的纠缠分发协议（entanglement distribution protocols）主要分为两类，即基于发射型与基于散射型，二者各有优劣。一方面，搭载谐振腔或波导的基于散射型协议速率较快，但对硬件要求严苛，需配备高效集成环行器或强波导耦合结构。另一方面，基于发射型实验平台虽具备实验可行性，但迄今仍依赖贝尔对融合（Bell-pair fusion）技术，且大量使用低速两量子比特存储门（two-qubit memory gates），将容错阈值限制在约0.16%。本文中，我们针对一种采用基于发射型纠缠方案的全分布式表面码（fully distributed surface code）展开研究，该方案可单次生成格林伯格-霍恩-蔡林格（Greenberger-Horne-Zeilinger, GHZ）态，无需执行贝尔对融合操作。我们证实，所提出的光学装置可生成贝尔对（Bell pairs）、W态（W states）以及GHZ态，可支持基于存储与光学的两类协议来蒸馏高保真GHZ态，且成功率得到显著提升。此外，我们提出的协议彻底摒弃了对基于存储的两量子比特门的需求，在适度升级硬件的前提下可将阈值提升至约0.19%，若配备光子数分辨探测器（photon-number-resolving detectors）则可进一步将阈值提升至约0.24%以上。上述结果证实了基于发射型架构实现可扩展容错运行的可行性。