[论文解读] Quantum Optical Convolutional Neural Network: A Novel Image Recognition Framework for Quantum Computing

Rishab Parthasarathy, Rohan Tan Bhowmik|arXiv (Cornell University)|Dec 19, 2020

Quantum Computing Algorithms and Architecture参考文献 28被引用 46

一句话总结

本文提出了一种量子光学卷积神经网络（QOCNN），这是一种新颖的混合量子-光学框架，将量子卷积层与池化层同光学神经网络相结合，用于图像识别。在MNIST数据集上的评估显示，QOCNN的准确率与经典模型和光学模型相当，同时在未来的量子硬件上展现出多个数量级的理论计算效率提升。

ABSTRACT

Large machine learning models based on Convolutional Neural Networks (CNNs) with rapidly increasing number of parameters, trained with massive amounts of data, are being deployed in a wide array of computer vision tasks from self-driving cars to medical imaging. The insatiable demand for computing resources required to train these models is fast outpacing the advancement of classical computing hardware, and new frameworks including Optical Neural Networks (ONNs) and quantum computing are being explored as future alternatives. In this work, we report a novel quantum computing based deep learning model, the Quantum Optical Convolutional Neural Network (QOCNN), to alleviate the computational bottleneck in future computer vision applications. Using the popular MNIST dataset, we have benchmarked this new architecture against a traditional CNN based on the seminal LeNet model. We have also compared the performance with previously reported ONNs, namely the GridNet and ComplexNet, as well as a Quantum Optical Neural Network (QONN) that we built by combining the ComplexNet with quantum based sinusoidal nonlinearities. In essence, our work extends the prior research on QONN by adding quantum convolution and pooling layers preceding it. We have evaluated all the models by determining their accuracies, confusion matrices, Receiver Operating Characteristic (ROC) curves, and Matthews Correlation Coefficients. The performance of the models were similar overall, and the ROC curves indicated that the new QOCNN model is robust. Finally, we estimated the gains in computational efficiencies from executing this novel framework on a quantum computer. We conclude that switching to a quantum computing based approach to deep learning may result in comparable accuracies to classical models, while achieving unprecedented boosts in computational performances and drastic reduction in power consumption.

研究动机与目标

• 解决训练大规模深度学习模型用于计算机视觉时日益增长的计算瓶颈问题。
• 探索一种结合量子计算与光学神经网络的新混合框架，以提升效率。
• 设计并基准测试一种新型架构——QOCNN，该架构将量子卷积与池化层同光学非线性特性相融合。
• 在MNIST数据集上评估QOCNN相对于经典、光学及量子基线模型的鲁棒性与性能表现。
• 估算在未来的量子硬件上执行QOCNN时，理论计算效率相较于经典框架的提升幅度。

提出的方法

• 提出一种混合QOCNN框架，将量子卷积层与光学神经网络组件融合，用于图像特征提取。
• 使用经过修改的MNIST数据集，其中每个28×28的图像被编码为392个复数，表示通过像素叠加的单光子Fock态。
• 利用量子线路实现卷积与池化操作，采用基于量子比特的矩阵乘法与酉变换。
• 在光学网络中引入基于量子的正弦非线性（如sin(x)），灵感源自ComplexNet与QONN架构。
• 在经典硬件上模拟QOCNN模型，以LeNet（经典CNN）、GridNet、ComplexNet以及带有sin(x)非线性的自定义QONN为基准进行性能对比。
• 采用准确率、混淆矩阵、ROC曲线及马修斯相关系数（MCC）评估模型，分析其鲁棒性与泛化能力。

实验结果

研究问题

• RQ1 量子-光学卷积神经网络是否能在MNIST上实现与经典及光学深度学习模型相当的图像识别准确率？
• RQ2 与纯光学或经典模型相比，量子卷积与池化层的融合对模型性能与鲁棒性有何影响？
• RQ3 相较于经典框架，未来量子硬件上执行QOCNN可实现多大程度的理论计算效率提升？
• RQ4 所提出的QOCNN模型在鲁棒性方面表现如何，依据ROC曲线与混淆矩阵衡量？
• RQ5 QOCNN框架中基于量子的非线性与矩阵运算在多大程度上降低了内存与计算复杂度？

主要发现

• QOCNN在MNIST测试集上达到了97.8%的准确率，与经典LeNet（97.6%）及其他基线模型相当。
• ROC曲线分析表明，QOCNN在所有数字类别上均保持高鲁棒性，曲线下面积（AUC）值始终高于0.95。
• 该模型展现出良好的泛化能力，混淆矩阵显示对角线主导性强，非对角线误分类率低。
• 理论分析表明，对于10层网络、批量大小200、输入规模10,000的情况，QOCNN在前向与反向传播中可实现较经典模型高达200倍的效率提升。
• 在量子系统中，内存使用量预计按O(L(log n + log b))缩放，相较经典模型的O(n²L)大幅降低，表明参数存储需求显著减少。
• 该框架在未来的容错NISQ时代量子硬件上执行时，理论上具备实现矩阵乘法速度提升多个数量级及功耗降低的潜力。