Generalization Study of Quantum Neural Network

TL;DR

This paper investigates a quantum neural network model based on quantum gates, demonstrating that its unitary operations and flatter parameter space lead to better generalization compared to classical neural networks, validated on public datasets.

Contribution

It introduces a quantum neural network model with unitary operations and analyzes its generalization advantages over classical neural networks.

Findings

Quantum neural network has a flatter parameter space.

The model exhibits better generalization on public datasets.

Quantum model outperforms classical neural networks with similar structure.

Abstract

Generalization is an important feature of neural network, and there have been many studies on it. Recently, with the development of quantum compu-ting, it brings new opportunities. In this paper, we studied a class of quantum neural network constructed by quantum gate. In this model, we mapped the feature data to a quantum state in Hilbert space firstly, and then implement unitary evolution on it, in the end, we can get the classification result by im-plement measurement on the quantum state. Since all the operations in quan-tum neural networks are unitary, the parameters constitute a hypersphere of Hilbert space. Compared with traditional neural network, the parameter space is flatter. Therefore, it is not easy to fall into local optimum, which means the quantum neural networks have better generalization. In order to validate our proposal, we evaluated our model on three public datasets, the results demonstrated that our model has better generalization than the classical neu-ral network with the same structure.