  We introduce and analyze a novel quantum machine learning model motivated by
convolutional neural networks. Our quantum convolutional neural network (QCNN)
makes use of only $O(\log(N))$ variational parameters for input sizes of $N$
qubits, allowing for its efficient training and implementation on realistic,
near-term quantum devices. The QCNN architecture combines the multi-scale
entanglement renormalization ansatz and quantum error correction. We explicitly
illustrate its potential with two examples. First, QCNN is used to accurately
recognize quantum states associated with 1D symmetry-protected topological
phases. We numerically demonstrate that a QCNN trained on a small set of
exactly solvable points can reproduce the phase diagram over the entire
parameter regime and also provide an exact, analytical QCNN solution. As a
second application, we utilize QCNNs to devise a quantum error correction
scheme optimized for a given error model. We provide a generic framework to
simultaneously optimize both encoding and decoding procedures and find that the
resultant scheme significantly outperforms known quantum codes of comparable
complexity. Finally, potential experimental realization and generalizations of
QCNNs are discussed.
