Quantum Hamiltonian embedding of images for data reuploading classifiers

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 a 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 (Schuld and Killoran 2022 PRX Quantum 3(3):030101.). 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 (Bowles et al. 2023). 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 (Pérez-Salinas et al. 2020 Quantum 4(226):226) with the quantum Hamiltonian data embedding unitary (Schuld and Petruccione 2021). Through numerical experiments on image datasets, including the famous MNIST and FashionMNIST datasets, we demonstrate that our model outperforms the quantum convolutional neural network (QCNN) (Cong et al. 2019 Nat Phys 15(12):1273–1278) 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.