Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regression

Abstract

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 reduction of classical inputs is concerned. In this work, we first put forth an end-to-end quantum neural network, namely, 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.

Exploiting Low-Rank Tensor-Train Deep Neural Networks Based on Riemannian Gradient Descent With Illustrations of Speech Processing

“…In doing so, a localized low-complexity speech processing system on local devices can maintain the baseline performance. Thus, it motivates us to design a low-complexity deep model without losing its capability in terms of representation and generalization powers [3]- [5].…”