论文标题
基于量子电路的功能回归的理论错误性能分析
Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regression
论文作者
论文摘要
嘈杂的中间尺度量子（NISQ）设备可以实现量子神经网络（QNN）的变分量子电路（VQC）。尽管基于VQC的QNN在许多机器学习任务中都取得了成功，但VQC的表示和泛化能力仍需要进一步研究，尤其是在涉及经典输入的维度时。在这项工作中，我们首先提出了一个端到端量子神经网络TTN-VQC，该网络由基于张量 - 训练网络（TTN）的量子张量网络组成，用于降低维数和用于功能回归的VQC。然后，我们旨在从表示和泛化能力方面对TTN-VQC进行错误性能分析。我们还通过利用polyak-lojasiewicz（PL）条件来表征TTN-VQC的优化属性。此外，我们在手写数字分类数据集上进行了功能回归的实验，以证明我们的理论分析是合理的。
The noisy intermediate-scale quantum (NISQ) devices enable the implementation of the variational quantum circuit (VQC) for quantum neural networks (QNN). Although the VQC-based QNN has succeeded in many machine learning tasks, the representation and generalization powers of VQC still require further investigation, particularly when the dimensionality of classical inputs is concerned. In this work, we first put forth an end-to-end quantum neural network, TTN-VQC, which consists of a quantum tensor network based on a tensor-train network (TTN) for dimensionality reduction and a VQC for functional regression. Then, we aim at the error performance analysis for the TTN-VQC in terms of representation and generalization powers. We also characterize the optimization properties of TTN-VQC by leveraging the Polyak-Lojasiewicz (PL) condition. Moreover, we conduct the experiments of functional regression on a handwritten digit classification dataset to justify our theoretical analysis.
