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arXiv 2408.03351quant-phcs.LG
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采用混合量子-经典方法的MNIST分类量子迁移学习

Quantum Transfer Learning for MNIST Classification Using a Hybrid Quantum-Classical Approach

Soumyadip Sarkar(独立研究者)

Soumyadip Sarkar

AI总结:

本研究提出混合量子-经典的MNIST分类模型,通过自编码器与PCA降维将图像特征编码到5量子比特态,经量子电路生成增强特征后用经典网络分类,验证了量子计算融入分类流程的可行性,但准确率暂低于纯经典基线。

摘要:

我们实现了一种用于图像分类的混合量子-经典模型,该模型将MNIST数字图像压缩到低维特征空间,随后将这些特征映射到5量子比特的量子态上。首先,自编码器(autoencoder)将每张28×28的图像(784像素)压缩为64维的潜在向量,以最小的重构误差保留数字的显著特征。我们使用主成分分析(Principal Component Analysis, PCA)进一步将潜在表示降维至5个主成分,以匹配可用的5个量子比特。这5个特征被编码为5量子比特量子电路中的旋转角度。量子特征图施加与特征值成比例的单量子比特旋转(R_y门),随后施加Hadamard门和级联的纠缠CNOT门,以生成非直积纠缠态。对5量子比特态进行测量会得到基态结果上的32维概率分布,该分布用作分类的量子增强特征向量。随后,在这些32维量子特征向量上训练带有softmax输出的经典神经网络,以预测数字类别。我们在MNIST数据集上评估了该混合模型,并将其与使用64维自编码器潜在特征进行分类的纯经典基线模型进行对比。结果表明,混合模型能够成功完成数字分类,证明了将量子计算整合到分类流程中的可行性,不过其准确率(测试数据上约75%)目前低于经典基线(在相同压缩数据上约98%)。

英文摘要:

We implement a hybrid quantum-classical model for image classification that compresses MNIST digit images into a low-dimensional feature space and then maps these features onto a 5-qubit quantum state. First, an autoencoder compresses each $28\times28$ image (784 pixels) into a 64-dimensional latent vector, preserving salient features of the digit with minimal reconstruction error. We further reduce the latent representation to 5 principal components using Principal Component Analysis (PCA), to match the 5 available qubits. These 5 features are encoded as rotation angles in a quantum circuit with 5 qubits. The quantum feature map applies single-qubit rotations ($R_y$ gates) proportional to the feature values, followed by a Hadamard gate and a cascade of entangling CNOT gates to produce a non-product entangled state. Measuring the 5-qubit state yields a 32-dimensional probability distribution over basis outcomes, which serves as a quantum-enhanced feature vector for classification. A classical neural network with a softmax output is then trained on these 32-dimensional quantum feature vectors to predict the digit class. We evaluate the hybrid model on the MNIST dataset and compare it to a purely classical baseline that uses the 64-dimensional autoencoder latent features for classification. The results show that the hybrid model can successfully classify digits, demonstrating the feasibility of integrating quantum computing in the classification pipeline, although its accuracy (about 75\% on test data) currently falls below the classical baseline (about 98\% on the same compressed data).

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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