Toward Trainability of Quantum Neural Networks

TL;DR

This paper addresses the trainability issues of quantum neural networks by proposing structured architectures that mitigate vanishing gradients, supported by theoretical guarantees and empirical demonstrations of improved convergence and accuracy.

Contribution

It introduces tree tensor and step controlled architectures for QNNs, providing theoretical analysis and numerical evidence of enhanced trainability over random structures.

Findings

Gradients vanish polynomially with qubit number in proposed architectures

Structured QNNs achieve faster convergence in binary classification tasks

Proposed architectures outperform random QNNs in accuracy and training speed

Abstract

Quantum Neural Networks (QNNs) have been recently proposed as generalizations of classical neural networks to achieve the quantum speed-up. Despite the potential to outperform classical models, serious bottlenecks exist for training QNNs; namely, QNNs with random structures have poor trainability due to the vanishing gradient with rate exponential to the input qubit number. The vanishing gradient could seriously influence the applications of large-size QNNs. In this work, we provide a viable solution with theoretical guarantees. Specifically, we prove that QNNs with tree tensor and step controlled architectures have gradients that vanish at most polynomially with the qubit number. We numerically demonstrate QNNs with tree tensor and step controlled structures for the application of binary classification. Simulations show faster convergent rates and better accuracy compared to QNNs with random structures.