噪声环境下基于纠缠纯化的鲁棒二维簇态量子网络编码

Robust Quantum Network Coding on 2D Cluster States via Entanglement Purification in Noisy Environments

摘要: 基于测量的量子计算(MBQC)为量子网络编码(QNC)提供了高效的并行处理框架，但现有基于二维簇态的QNC方案多假设理想信道，在实际偏置Pauli噪声环境下，其纠缠保真度会发生指数级衰减，难以满足量子密钥分发等应用的安全阈值。针对这一物理实现瓶颈，文章提出了一种抗噪性增强的鲁棒量子网络编码架构。该方案在空间复用的14粒子蝶形网络模型基础上，创新性地引入了改进的DEJMPS纠缠纯化协议。通过在端节点预先执行局部幺正旋转，将信道中占主导的相位误差转化为易于检测的形式，从而在同等资源消耗下实现了对偏置噪声的有效抑制。基于Qiskit的系统级数值仿真不仅验证了该方案相较于传统纯化协议具有显著更高的输出保真度，还首次定量评估了端节点本地量子门误差对纯化鲁棒性的影响。结果表明，只要本地操作的去极化误差处于特定容错阈值内，该架构便能保持正向的纠缠浓缩增益。研究有效扩展了量子网络编码的适用噪声边界，为近期含噪量子(NISQ)设备上的高保真量子通信部署提供了关键的架构参考。

Abstract: Measurement-based quantum computation (MBQC) provides an efficient parallel processing framework for quantum network coding (QNC). However, existing QNC schemes based on two-dimensional (2D) cluster states mostly assume ideal channels. In practical biased Pauli noise environments, their entanglement fidelity decays exponentially, making it difficult to meet the security thresholds for applications such as quantum key distribution (QKD). To address this physical implementation bottleneck, this paper proposes a robust quantum network coding architecture with enhanced noise resilience. Based on a spatially multiplexed 14-qubit butterfly network model, this scheme innovatively introduces the modified DEJMPS entanglement purification protocol. By performing local unitary rotations at the end nodes beforehand, this scheme transforms the dominant phase errors in the channel into easily detectable forms, thereby achieving effective suppression of biased noise under the same resource consumption. System-level numerical simulations based on Qiskit not only verify that this scheme achieves significantly higher output fidelity compared to traditional purification protocols, but also quantitatively evaluate the impact of local quantum gate errors at the end nodes on the purification robustness for the first time. The results show that as long as the depolarizing errors of local operations are within a specific fault-tolerant threshold, the architecture can maintain a positive entanglement concentration gain. The research in this paper effectively expands the applicable noise boundaries of quantum network coding, providing a crucial architectural reference for the deployment of high-fidelity quantum communication on noisy intermediate-scale quantum (NISQ) devices.