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I am currently reading the paper arXiv:1810.03787. The authors claim that QCNN uses only $O(\log N)$ variational parameters, where $N$ is the number of qubits. However, I am having difficulty understanding how to count the number of variational parameters for an input size of $N$ qubits.

Furthermore, in the case of Convolutional Neural Networks (CNNs), to my knowledge, the number of parameters is determined by the structure of the CNN rather than the size of the input. Could you help me revise this for clarity?

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    $\begingroup$ There is a commonly used CNN where the image dimension is halved each time, 256x256 -> 128x128 -> 64x64 -> Since each layer uses a small number of kernel parameters, the total number of parameters should grow by approximately $\log N$ of the original image size. $\endgroup$
    – James
    Commented Sep 23 at 12:42
  • $\begingroup$ What can a quantum CNN do / is useful for? $\endgroup$
    – James
    Commented Sep 23 at 12:42

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