Data/software underlying the publication: Fault-tolerant structures for measurement-based quantum computation on a network

In this work, we introduce a method to construct fault-tolerant measurement-based quantum computation (MBQC) architectures and numerically estimate their performance over various types of networks. A possible application of such a paradigm is distributed quantum computation, where separate computing nodes work together on a fault-tolerant computation through entanglement. We gauge error thresholds of the architectures with an efficient stabilizer simulator to investigate the resilience against both circuit-level and network noise. We show that, for both monolithic (i.e., non-distributed) and distributed implementations, an architecture based on the diamond lattice may outperform the conventional cubic lattice. Moreover, the high erasure thresholds of non-cubic lattices may be exploited further in a distributed context, as their performance may be boosted through entanglement distillation by trading in entanglement success rates against erasure errors during the error decoding process. These results highlight the significance of lattice geometry in the design of fault-tolerant measurement-based quantum computing on a network, emphasizing the potential for constructing robust and scalable distributed quantum computers.

本研究提出了一种构建容错基于测量的量子计算（fault-tolerant measurement-based quantum computation, MBQC）架构的方法，并对其在各类网络中的性能开展数值评估。该计算范式的一项潜在应用为分布式量子计算：多个独立计算节点可通过纠缠协同完成容错量子计算任务。我们借助高效稳定子模拟器（stabilizer simulator）对该类架构的错误阈值进行量化评估，以探究其对电路级噪声（circuit-level noise）与网络级噪声（network-level noise）的抗扰能力。研究结果显示，无论是整体式（即非分布式）实现还是分布式实现，基于菱形晶格（diamond lattice）的架构性能均优于传统立方晶格（cubic lattice）。此外，非立方晶格具备较高的擦除错误（erasure errors）阈值，这一特性可在分布式场景中进一步挖掘利用：通过纠缠蒸馏（entanglement distillation），可在错误解码过程中以纠缠成功率为代价，换取对擦除错误的抵御能力，从而进一步提升系统整体性能。上述研究结果凸显了晶格几何构型在网络型容错基于测量的量子计算架构设计中的关键意义，为构建鲁棒且可扩展的分布式量子计算机指明了潜在方向。