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.

我们介绍了一种新型的基于卷积神经网络的量子机器学习模型，并进行了分析。它采用了多尺度纠缠重正化基矢和量子纠错技术，具有高效的训练和实现能力，并展示了两个例子来证明其潜力。首先，我们使用 QCNN 准确识别了与一维对称保护拓扑相关的量子态，并发现其在整个参数范围内都能复制相图。其次，我们利用 QCNN 开发了一种优化给定误差模型的量子纠错方案，并发现其显著优于已知的可比较复杂度的量子码。最后，我们讨论了 QCNN 的潜在实验实现和拓展。