QCNN layers equivariant under pixel cyclic shifts are exactly characterized as Fourier-mode multiplexers after QFT, enabling a deep network with constant expected gradient norm at initialization.
In many spatial problems, the same local pattern is applied at every position: each output feature at locationkdepends on inputs in the same relative way at any location
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Pixel-Translation-Equivariant Quantum Convolutional Neural Networks via Fourier Multiplexers
QCNN layers equivariant under pixel cyclic shifts are exactly characterized as Fourier-mode multiplexers after QFT, enabling a deep network with constant expected gradient norm at initialization.