基于Bures-Uhlmann几何的异构噪声客户端量子联邦学习
Quantum Federated Learning Based on Bures--Uhlmann Geometry for Heterogeneous Noisy Clients
浏览论文内容
中文总结 AI 辅助
该研究针对异构噪声客户端的量子联邦学习问题，基于Bures-Uhlmann几何提出含局部预条件子与动态权重聚合规则的方法，经囚禁离子模拟器验证其准确率优于标准联邦平均算法。
中文摘要 AI 辅助
量子联邦学习可在量子设备间开展协作式模型训练且无需共享原始数据，但它面临有噪量子设备固有的数据与硬件异构性问题。利用量子几何张量是一种自然的解决方案，不过纯态方法与对角近似会丢弃编码参数不相容性的关联信息。为解决该问题，我们将参数空间几何扩展到有噪客户端实际制备的混合态；所得混合态几何张量的实部为Bures度量，用于衡量物理态随参数变化的速率，虚部为平均Uhlmann曲率，用于量化同时估计多个参数的不相容性。据此，我们采用Bures度量作为局部预条件子，并利用平均Uhlmann曲率开发出可实现精度的聚合规则，该规则会动态降低不可靠客户端的权重。此外，我们通过证明收敛定理与方差主导命题建立了理论保证；在囚禁离子量子模拟器上的实证评估表明，所提方法在各类设备异构性条件下均能保持高准确率，且优于标准联邦平均算法，后者在强噪声下准确率会下降。
英文摘要
Quantum federated learning enables collaborative model training across quantum devices without sharing raw data, and it faces the data and hardware heterogeneity inherent to noisy quantum devices. Utilizing the quantum geometric tensor is a natural remedy, yet pure-state approaches and diagonal approximations discard the correlations that encode parameter incompatibility. To address this, we extend the parameter-space geometry to the mixed states that noisy clients actually prepare. The real part of the resulting mixed-state geometric tensor is the Bures metric, which measures how fast the physical state changes under parameter variation, and the imaginary part is the mean Uhlmann curvature, which quantifies the incompatibility of estimating multiple parameters simultaneously. Accordingly, we employ the Bures metric as a local preconditioner and use the mean Uhlmann curvature to develop an achievable-precision aggregation rule that dynamically down-weights unreliable clients. Furthermore, we establish theoretical guarantees by proving a convergence theorem and a variance-dominance proposition. Empirical evaluations on a trapped-ion quantum emulator demonstrate that the proposed method maintains high accuracy across diverse device-heterogeneity conditions and outperforms standard federated averaging, whose accuracy degrades under strong noise.
