基于自适应非局域可观测量的量子神经网络准极分解
Quasi-polar Decomposition of Quantum Neural Networks via Adaptive Non-local Observables
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中文总结 AI 辅助
该研究采用对角自适应非局域可观测量（DANO）对量子神经网络进行准极分解，将训练转化为谱与李代数空间的轨迹，实验证实其径向谱及角坐标分量与分类准确率相关，为表征量子模型行为提供了新视角。
中文摘要 AI 辅助
我们采用对角自适应非局域可观测量（Diagonal Adaptive Non-local Observables，DANO）作为变分量子电路模型演化研究的典型分解方式。将每个学习到的可观测量分离为对角谱和幺正基，可得到准极描述：谱权重被视为径向坐标，幺正电路通过李群识别充当角坐标，这将训练过程转化为谱空间与李代数空间中的轨迹。针对两个分类任务的实验表明，DANO径向谱展开与准确率相关，DANO角坐标揭示出一个与准确率相关的主导分量，该框架为表征量子模型行为提供了不同视角。
英文摘要
We use Diagonal Adaptive Non-local Observables (DANO) as a canonical decomposition for studying Variational Quantum Circuit model evolution. Separating each learned observable into a diagonal spectrum and a unitary basis gives a quasi-polar description: the spectral weights are viewed as radial coordinates, while the unitary circuit serves as angular coordinates through Lie group identifications. This turns the training process into a trajectory in spectral and Lie-algebra space. Experiments on two classification tasks show that DANO radial spectral expansion correlates with accuracy. DANO angle coordinates reveal a dominant accuracy-correlated component. The framework provides a different perspective to characterize quantum model behavior.
