Quantum Hamiltonian Embedding of Images for Data Reuploading Classifiers

As a key application area of quantum computing, quantum machine learning [6] has received considerable attention as an area that may achieve a potential quantum advantage compared to classical machine learning/deep learning algorithms through runtime acceleration. The quest for achieving such acceleration has become a standard motivation while developing quantum machine learning algorithms, evidenced by the use of efficient quantum subroutines that could accelerate linear algebra calculations, such as the quantum principal component analysis algorithm (qPCA), which involves calculations of the eigenvalues and eigenvectors of a covariance matrix by quantum phase estimation [7]. Unlike principal component analysis and kernel methods, which are often referred to as statistical learning algorithms, neural networks, with their ability to discover hidden patterns in large-scale unstructured datasets such as image and natural language, have gained momnentum since the invention of AlexNet [8], and have become the foundation of modern artificial intelligence applications such as ChatGPT-4 [9]. However, since time complexity is rarely the first priority when designing novel deep neural network architectures, which often rely on intuition and even inspirations from biological neural networks, it becomes less obvious that quantum computing should find any advantage or utility in deep learning and AI. Although recent research has attempted to integrate properties that are unique to quantum systems, such as contextuality, into the design of quantum machine learning models for specific types of tasks that could lead to quantum advantage [2], few studies have taken the intuition behind successful deep learning models into account and how to integrate them into quantum machine learning models. In this paper, we aim to bridge this gap by bringing such intuition to the design of quantum machine learning models, especially quantum neural networks, via numerical experiments for the design of a quantum machine learning model for benchmarking image processing tasks. Our main contributions in this paper are as follow: Construction of a quantum classifier based on the quantum Hamiltonian embedding approach and the data reuploading circuit; Results from numerical experiments show that the proposed model could outperform the baseline quantum convolutional neural network model [5]; Based on the model design process and the numerical experiments, we lay out a set of principles for future quantum machine learning (QML) model design.