With the beginning of the noisy intermediate-scale quantum (NISQ) era,
quantum neural network (QNN) has recently emerged as a solution for the
problems that classical neural networks cannot solve. Moreover, QCNN is
attracting attention as the next generation of QNN because it can process
high-dimensional vector input. However, due to the nature of quantum computing,
it is difficult for the classical QCNN to extract a sufficient number of
features. Motivated by this, we propose a new version of QCNN, named scalable
quantum convolutional neural network (sQCNN). In addition, using the fidelity
of QC, we propose an sQCNN training algorithm named reverse fidelity training
(RF-Train) that maximizes the performance of sQCNN.

提出一种新型的可伸缩量子卷积神经网络 (sQCNN)，并提供了一种名为反保真度训练 (RF-Train) 的训练算法用于提高 sQCNN 的性能。该网络为量子神经网络 (QNN) 的一种进化，拥有处理高维向量输入的能力，并且可以解决传统 QNN 的局限性。

可扩展的量子卷积神经网络

Scalable Quantum Convolutional Neural Networks

Quantum computing is a new computational paradigm that promises applications
in several fields, including machine learning. In the last decade, deep
learning, and in particular Convolutional neural networks (CNN), have become
essential for applications in signal processing and image recognition. Quantum
deep learning, however remains a challenging problem, as it is difficult to
implement non linearities with quantum unitaries. In this paper we propose a
quantum algorithm for applying and training deep convolutional neural networks
with a potential speedup. The quantum CNN (QCNN) is a shallow circuit,
reproducing completely the classical CNN, by allowing non linearities and
pooling operations. The QCNN is particularly interesting for deep networks and
could allow new frontiers in image recognition, by using more or larger
convolution kernels, larger or deeper inputs. We introduce a new quantum
tomography algorithm with $\ell_{\infty}$ norm guarantees, and new applications
of probabilistic sampling in the context of information processing. We also
present numerical simulations for the classification of the MNIST dataset to
provide practical evidence for the efficiency of the QCNN.

该研究论文提出了一种基于量子计算的卷积神经网络（QCNN）算法，能够应用和训练深度 CNN，并通过引入非线性和池化操作打破传统的限制，以更高效地进行图像识别，同时也介绍了新的量子测量及概率采样算法。

深度卷积神经网络的量子算法

Quantum Algorithms for Deep Convolutional Neural Networks

Neural networks in the real domain have been studied for a long time and
achieved promising results in many vision tasks for recent years. However, the
extensions of the neural network models in other number fields and their
potential applications are not fully-investigated yet. Focusing on color
images, which can be naturally represented as quaternion matrices, we propose a
quaternion convolutional neural network (QCNN) model to obtain more
representative features. In particular, we redesign the basic modules like
convolution layer and fully-connected layer in the quaternion domain, which can
be used to establish fully-quaternion convolutional neural networks. Moreover,
these modules are compatible with almost all deep learning techniques and can
be plugged into traditional CNNs easily. We test our QCNN models in both color
image classification and denoising tasks. Experimental results show that they
outperform the real-valued CNNs with same structures.

通过使用四元数矩阵表示，我们提出了一个四元数卷积神经网络（QCNN）模型来在彩色图像分类和去噪任务中得到更具代表性的特征，并测试结果表明该模型优于具有相同结构的实值卷积神经网络。

四元数卷积神经网络

Quaternion Convolutional Neural Networks

Convolutional neural networks (CNN) have recently achieved state-of-the-art
results in various applications. In the case of image recognition, an ideal
model has to learn independently of the training data, both local dependencies
between the three components (R,G,B) of a pixel, and the global relations
describing edges or shapes, making it efficient with small or heterogeneous
datasets. Quaternion-valued convolutional neural networks (QCNN) solved this
problematic by introducing multidimensional algebra to CNN. This paper proposes
to explore the fundamental reason of the success of QCNN over CNN, by
investigating the impact of the Hamilton product on a color image
reconstruction task performed from a gray-scale only training. By learning
independently both internal and external relations and with less parameters
than real valued convolutional encoder-decoder (CAE), quaternion convolutional
encoder-decoders (QCAE) perfectly reconstructed unseen color images while CAE
produced worst and gray-scale versions.

本文研究基于多元代数的四元数卷积神经网络在彩色图像重建任务上的成功原因，发现其可以更好地学习内部和外部关系以及更少的参数数量与灰度训练的情况下，在重建未看到的彩色图像上表现较好。