Data/software underlying the publication: Thresholds for the distributed surface code in the presence of memory 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、容错量子计算的进程中，分布式量子计算机是极具前景的候选方案。此类系统既可通过大规模量子网络实现，亦可集成于搭载紧密排布节点的单芯片之中。本研究提出一种基于分布式环面表面码（distributed toric surface code）的存储信道数值模拟框架：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（GHZ）态的品质。我们定量研究了存储退相干的影响，并评估了针对退相干程度定制的GHZ态生成协议的优势。我们以金刚石中的色心为具体研究对象，依托基于氮-空位中心实验表征构建的模型，应用上述框架开展相关研究。对于金刚石色心而言，纠缠生成过程中的相干时间相较于闲置量子比特的相干时间低数个数量级。此类相干时间是实际应用的限制因素，但此前的表面码模拟并未将其纳入考量范围。将受限相干时间作为一项关键噪声因素纳入考量，意味着必须在模拟中融入真实的操作时长，并引入操作调度策略。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至原先的三分之一。我们还在纠缠生成速率与退相干速率的比值中找到了4×10²的阈值，为实验进展确立了基准标杆。