Quantum convolutional neural networks (QCNNs) represent a promising approach
in quantum machine learning, paving new directions for both quantum and
classical data analysis. This approach is particularly attractive due to the
absence of the barren plateau problem, a fundamental challenge in training
quantum neural networks (QNNs), and its feasibility. However, a limitation
arises when applying QCNNs to classical data. The network architecture is most
natural when the number of input qubits is a power of two, as this number is
reduced by a factor of two in each pooling layer. The number of input qubits
determines the dimensions (i.e. the number of features) of the input data that
can be processed, restricting the applicability of QCNN algorithms to
real-world data. To address this issue, we propose a QCNN architecture capable
of handling arbitrary input data dimensions while optimizing the allocation of
quantum resources such as ancillary qubits and quantum gates. This optimization
is not only important for minimizing computational resources, but also
essential in noisy intermediate-scale quantum (NISQ) computing, as the size of
the quantum circuits that can be executed reliably is limited. Through
numerical simulations, we benchmarked the classification performance of various
QCNN architectures when handling arbitrary input data dimensions on the MNIST
and Breast Cancer datasets. The results validate that the proposed QCNN
architecture achieves excellent classification performance while utilizing a
minimal resource overhead, providing an optimal solution when reliable quantum
computation is constrained by noise and imperfections.

该论文介绍了一个能够处理任意输入数据维度的量子卷积神经网络 (QCNN) 架构，优化了量子资源的分配，达到了优秀的分类性能，同时最小化了资源开销，为噪声和不完美情况下可靠量子计算提供了最佳解决方案。

针对任意数据维度优化量子卷积神经网络结构

Optimizing Quantum Convolutional Neural Network Architectures for  Arbitrary Data Dimension

Variational quantum circuit (VQC) is a promising approach for implementing
quantum neural networks on noisy intermediate-scale quantum (NISQ) devices.
Recent studies have shown that a tensor-train network (TTN) for VQC, namely
TTN-VQC, can improve the representation and generalization powers of VQC.
However, the Barren Plateau problem leads to the gradients of the cost function
vanishing exponentially small as the number of qubits increases, making it
difficult to find the optimal parameters for the VQC. To address this issue, we
put forth a new learning approach called Pre+TTN-VQC that builds upon the
TTN-VQC architecture by incorporating a pre-trained TTN to alleviate the Barren
Plateau problem. The pre-trained TTN allows for efficient fine-tuning of target
data, which reduces the depth of the VQC required to achieve good empirical
performance and potentially alleviates the training obstacles posed by the
Barren Plateau landscape. Furthermore, we highlight the advantages of
Pre+TTN-VQC in terms of representation and generalization powers by exploiting
the error performance analysis. Moreover, we characterize the optimization
performance of Pre+TTN-VQC without the need for the Polyak-Lojasiewicz
condition, thereby enhancing the practicality of implementing quantum neural
networks on NISQ devices. We conduct experiments on a handwritten digit
classification dataset to corroborate our proposed methods and theorems.

本文提出了一种名为 Pre+TTN-VQC 的学习方法，将一个预训练的张量列网络（TTN）集成到 TTN-VQC 架构中，以缓解 Barren Plateau 问题并提高量子神经网络的表示和概括能力，实验验证了该方法在手写数字分类中的有效性。