  Quantum machine learning is one of the most promising applications of quantum
computing in the Noisy Intermediate-Scale Quantum(NISQ) era. Here we propose a
quantum convolutional neural network(QCNN) inspired by convolutional neural
networks(CNN), which greatly reduces the computing complexity compared with its
classical counterparts, with $O((log_{2}M)^6) $ basic gates and $O(m^2+e)$
variational parameters, where $M$ is the input data size, $m$ is the filter
mask size and $e$ is the number of parameters in a Hamiltonian. Our model is
robust to certain noise for image recognition tasks and the parameters are
independent on the input sizes, making it friendly to near-term quantum
devices. We demonstrate QCNN with two explicit examples. First, QCNN is applied
to image processing and numerical simulation of three types of spatial
filtering, image smoothing, sharpening, and edge detection are performed.
Secondly, we demonstrate QCNN in recognizing image, namely, the recognition of
handwritten numbers. Compared with previous work, this machine learning model
can provide implementable quantum circuits that accurately corresponds to a
specific classical convolutional kernel. It provides an efficient avenue to
transform CNN to QCNN directly and opens up the prospect of exploiting quantum
power to process information in the era of big data.
