What can we learn from quantum convolutional neural networks?
Chukwudubem Umeano Annie E. Paine Vincent E. Elfving Oleksandr Kyriienko
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.