一种具有高效经典可模拟性的新型并行量子卷积神经网络架构

中文摘要 AI 辅助

本文研究了一种用于对来自修改后的国家标准与技术研究所（MNIST）数据集的图像进行二分类的新型量子卷积神经网络（QCNN）的实现。采用受先前QCNN和经典卷积神经网络（CNN）实现启发的新型架构，使用分层分区方法来实现一个QCNN电路，该电路在经典机器上对于大问题能够被高效近似和模拟。首先对原始图像进行分区，每个进程处理图像的较小部分并编码为独立状态，然后这些分区合并，状态包含两个分区的信息且进程数减半，重复此操作直到只剩一个进程，再降低状态维度直到只剩一个量子比特用于测量。利用这种方法，可并行使用多个进程来模拟大型QCNN程序，无需因量子比特数增加而使硬件需求呈指数增长。在工作中，用此方案训练了一个128量子比特的模型，这在无此新型架构时无法在任何经典超级计算机上运行。还通过在MNIST数据集上用少量量子比特训练并与无分区模型比较，探索了新模型架构对预测准确性的影响。初步发现表明，用此架构将图像分割成较小子图像不会降低模型性能，有时甚至会提高，可能是因为减少了分区过程中的贫瘠高原问题。

英文摘要

This work presents a study of an implementation of a novel Quantum Convolutional Neural Network (QCNN) for binary classification of images from the Modified National Institute of Standards and Technology (MNIST) dataset. Using a novel architecture inspired by previous QCNN and classical convolutional neural network (CNN) implementations, we use a hierarchical partitioning approach to implement a QCNN circuit that can be approximated and simulated efficiently on a classical machine for a large problem. First, the original image is partitioned such that each process handles a smaller portion of the image, which is encoded into independent states. Then, these partitions merge and combine, resulting in states that contain information from both partitions while halving the number of processes. After repeating this until one process remains, we reduce the dimensionality of the state until a single qubit remains for measurement. Using this approach, we can use multiple processes in parallel to simulate a large QCNN program without the need for exponentially growing hardware requirements as the number of qubits increases. In our work, we use this scheme to train a 128-qubit model, which is impossible to run on any classical supercomputer without the novel architecture. We also explore the impact of this new model architecture on prediction accuracy by training it to perform binary classification on the MNIST dataset with a small number of qubits, and comparing it to a model without partitioning. Our initial findings show that partitioning images into smaller sub-images with this architecture does not degrade the model's performance and sometimes even improves it, likely because it reduces the Barren plateaus issue in the partitioning process.

发表机构

• Department of Electrical Engineering（电气工程系）
• San José State University（桑乔州立大学）

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