We can learn from analyzing quantum convolutional neural networks (QCNNs)
that: 1) working with quantum data can be perceived as embedding physical
system parameters through a hidden feature map; 2) their high performance for
quantum phase recognition can be attributed to generation of a very suitable
basis set during the ground state embedding, where quantum criticality of spin
models leads to basis functions with rapidly changing features; 3) pooling
layers of QCNNs are responsible for picking those basis functions that can
contribute to forming a high-performing decision boundary, and the learning
process corresponds to adapting the measurement such that few-qubit operators
are mapped to full-register observables; 4) generalization of QCNN models
strongly depends on the embedding type, and that rotation-based feature maps
with the Fourier basis require careful feature engineering; 5) accuracy and
generalization of QCNNs with readout based on a limited number of shots favor
the ground state embeddings and associated physics-informed models. We
demonstrate these points in simulation, where our results shed light on
classification for physical processes, relevant for applications in sensing.
Finally, we show that QCNNs with properly chosen ground state embeddings can be
used for fluid dynamics problems, expressing shock wave solutions with good
generalization and proven trainability.

从分析量子卷积神经网络（QCNNs）中我们得出以下结论：1）利用量子数据可以通过隐藏特征映射来嵌入物理系统参数；2）它们在量子相识别方面的高性能可以归因于在地面态嵌入期间产生非常适合的基函数集，其中旋转模型的量子临界性导致具有快速变化特征的基函数；3）QCNNs 的汇集层负责选择那些可以有助于形成高性能决策边界的基函数，学习过程对应调整测量，使得少量量子比特算子映射到全寄存器观测量；4）QCNN 模型的泛化强依赖于嵌入类型，而基于傅立叶基准的旋转特征映射需要精心设计；5）基于有限测量次数的 QCNN 的准确性和泛化能力偏爱地面态嵌入和相关的物理信息模型。我们通过模拟展示了这些观点，我们的结果为感知应用中与物理过程分类有关的问题提供了启示。最后，我们展示了选择适当的地面态嵌入可以用于流体动力学问题的 QCNN，可以良好泛化并经过验证可训练。