Data/software underlying the publication: Thresholds for the distributed surface code in the presence of decoherence

In the search for scalable, fault-tolerant quantum computing, distributed quantum computers are promising candidates. These systems can be realized in large-scale quantum networks or condensed onto a single chip with closely situated nodes. We present a framework for numerical simulations of a memory channel using the distributed toric surface code, where each data qubit of the code is part of a separate node, and the error-detection performance depends on the quality of four-qubit Greenberger-Horne-Zeilinger (GHZ) states generated between the nodes. We quantitatively investigate the effect of memory decoherence and evaluate the advantage of GHZ creation protocols tailored to the level of decoherence. We do this by applying our framework for the particular case of color centers in diamond, employing models developed from experimental characterization of nitrogen-vacancy centers. For diamond color centers, coherence times during entanglement generation are orders of magnitude lower than coherence times of idling qubits. These coherence times represent a limiting factor for applications, but previous surface code simulations did not treat them as such. Introducing limiting coherence times as a prominent noise factor makes it imperative to integrate realistic operation times into simulations and incorporate strategies for operation scheduling. Our model predicts error probability thresholds for gate and measurement reduced by at least a factor of three compared to prior work with more idealized noise models. We also find a threshold of 4*10^2 in the ratio between the entanglement generation and the decoherence rates, setting a benchmark for experimental progress.

在探索可扩展、容错量子计算的研究中，分布式量子计算机是极具潜力的候选方案。此类系统既可通过大规模量子网络实现部署，也可集成于单芯片之上，搭载紧密排布的计算节点。我们提出了一套基于分布式环面表面码（distributed toric surface code）的记忆信道数值模拟框架：该编码的每个数据量子比特（qubit）均隶属于独立节点，其错误检测性能取决于节点间生成的四量子比特格林伯格-霍恩-蔡林格（Greenberger-Horne-Zeilinger, GHZ）态的质量。我们定量分析了记忆退相干效应，并评估了针对退相干水平定制的GHZ态生成协议的性能优势。
我们以金刚石色心为具体研究对象，采用基于氮空位中心（nitrogen-vacancy centers）实验表征结果构建的模型开展相关研究。对于金刚石色心而言，纠缠生成过程中的相干时间比空闲量子比特的相干时间低数个数量级。此类相干时间是制约实际应用的关键因素，但此前的表面码模拟并未将其作为核心噪声源纳入考量。将受限相干时间作为核心噪声因子纳入模型，意味着必须在模拟中引入符合实际的操作时长，并整合操作调度策略。
相较于采用更理想化噪声模型的前期研究，本模型预测的门操作与测量错误概率阈值至少降低至原有的1/3。我们还得到了纠缠生成速率与退相干速率比值的阈值为4×10²，该结果为实验研究的后续进展提供了基准参考。