What insights can quantum convolutional neural networks provide us?

[Submitted on 31 Aug 2023]

Download a PDF of the paper titled “What can we learn from quantum convolutional neural networks?” by Chukwudubem Umeano and 3 other authors

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Abstract: This paper analyzes quantum convolutional neural networks (QCNNs) and highlights the following findings: 1) Quantum data can be considered as embedding physical system parameters through a hidden feature map; 2) QCNNs perform well in quantum phase recognition due to the generation of a suitable basis set during ground state embedding, where quantum criticality of spin models produces basis functions with rapidly changing features; 3) Pooling layers in QCNNs select basis functions that contribute to forming a high-performing decision boundary, and the learning process involves adapting the measurement to map few-qubit operators to full-register observables; 4) Generalization of QCNN models depends on the type of embedding, with rotation-based feature maps requiring careful feature engineering using the Fourier basis; 5) Accuracy and generalization of QCNNs with limited shot readout favor ground state embeddings and physics-informed models. Simulation results demonstrate these points and their relevance to classification in physical processes, particularly in sensing applications. Additionally, QCNNs with properly chosen ground state embeddings show promise for fluid dynamics problems by accurately expressing shock wave solutions with good generalization and trainability.