Quantum Hamiltonian Embedding of Images for Data Reuploading Classifiers

TL;DR

This paper introduces a novel quantum neural network model using Hamiltonian data embedding and data reuploading, demonstrating significant performance improvements on image datasets like MNIST and FashionMNIST.

Contribution

It presents a new quantum neural network architecture based on data reuploading and Hamiltonian embedding, with six principles for quantum model design.

Findings

Outperforms quantum convolutional neural networks by up to 40% on MNIST.

Shows the effectiveness of Hamiltonian data embedding in quantum image classification.

Provides guidelines for designing quantum neural networks based on empirical principles.

Abstract

When applying quantum computing to machine learning tasks, one of the first considerations is the design of the quantum machine learning model itself. Conventionally, the design of quantum machine learning algorithms relies on the ``quantisation" of classical learning algorithms, such as using quantum linear algebra to implement important subroutines of classical algorithms, if not the entire algorithm, seeking to achieve quantum advantage through possible run-time accelerations brought by quantum computing. However, recent research has started questioning whether quantum advantage via speedup is the right goal for quantum machine learning [1]. Research also has been undertaken to exploit properties that are unique to quantum systems, such as quantum contextuality, to better design quantum machine learning models [2]. In this paper, we take an alternative approach by incorporating the heuristics and empirical evidences from the design of classical deep learning algorithms to the design of quantum neural networks. We first construct a model based on the data reuploading circuit [3] with the quantum Hamiltonian data embedding unitary [4]. Through numerical experiments on images datasets, including the famous MNIST and FashionMNIST datasets, we demonstrate that our model outperforms the quantum convolutional neural network (QCNN)[5] by a large margin (up to over 40% on MNIST test set). Based on the model design process and numerical results, we then laid out six principles for designing quantum machine learning models, especially quantum neural networks.