arXiv:2410.01252quant-phcs.LG2024-10被引 5

提出更省资源的对称量子卷积网络,提升训练效率与泛化能力。

Resource-efficient equivariant quantum convolutional neural networks

  • 通过分层并行结构,在池化层拆分电路以保留对称性
  • 测量资源减少量级与量子比特数相当,避免梯度消失问题
  • 适合资源受限的近中期量子设备上的机器学习任务

等变量子神经网络(QNN)是利用对称性提升机器学习性能的有前途的变分模型。尽管等变QNN在理论上取得进展,但其在近中期量子设备上的实现仍受计算资源限制。本文提出一种资源高效的等变量子卷积神经网络(QCNN)模型——等变分拆并行QCNN(sp-QCNN)。基于群论方法,将一般对称性编码至模型中,突破了以往sp-QCNN仅处理平移对称性的局限。通过在池化层拆分电路,在保持对称性的同时实现有效并行,显著提升可观测值及其梯度估计的测量效率,提升量级与量子比特数相当。该模型还表现出高可训练性和泛化性能,且无平坦谷现象。数值实验表明,在噪声量子数据分类任务中,等变sp-QCNN相比传统等变QCNN能以更少测量资源完成训练与泛化。研究结果推动了实用量子机器学习算法的发展。

原文摘要 · Abstract (English)

Equivariant quantum neural networks (QNNs) are promising variational models that exploit symmetries to improve machine learning capabilities. Despite theoretical developments in equivariant QNNs, their implementation on near-term quantum devices remains challenging due to limited computational resources. This study proposes a resource-efficient model of equivariant quantum convolutional neural networks (QCNNs) called equivariant split-parallelizing QCNN (sp-QCNN). Using a group-theoretical approach, we encode general symmetries into our model beyond the translational symmetry addressed by previous sp-QCNNs. We achieve this by splitting the circuit at the pooling layer while preserving symmetry. This splitting structure effectively parallelizes QCNNs to improve measurement efficiency in estimating the expectation value of an observable and its gradient by order of the number of qubits. Our model also exhibits high trainability and generalization performance, including the absence of barren plateaus. Numerical experiments demonstrate that the equivariant sp-QCNN can be trained and generalized with fewer measurement resources than a conventional equivariant QCNN in a noisy quantum data classification task. Our results contribute to the advancement of practical quantum machine learning algorithms.

量子机器学习对称性资源效率量子卷积

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