Theoretical error performance analysis for variational quantum circuit based functional regression

Abstract The noisy intermediate-scale quantum devices enable the implementation of variational circuit (VQC) for neural networks (QNN). Although VQC-based QNN has succeeded in many machine learning tasks, representation and generalization powers VQC still require further investigation, particularly when dimensionality classical inputs is concerned. In this work, we first put forth an end-to-end QNN, TTN-VQC, which consists a tensor network based on tensor-train (TTN) reduction functional regression. Then, aim at error performance analysis TTN-VQC terms powers. We also characterize optimization properties by leveraging Polyak-Lojasiewicz condition. Moreover, conduct experiments regression handwritten digit classification dataset to justify our theoretical analysis.