Quantum neural networks for medical data: A statistical analysis of quantum performance

Quantum information science explores the preparation, control, and manipulation of quantum states in physical systems, aiming to revolutionize information transmission and processing. This interdisciplinary field, encompassing quantum communication, computation, and information, represents a paradigm shift in understanding and utilizing information. Importantly, quantum computing holds the potential to address computational challenges that are intractable for classical systems, offering new frontiers for data science. The link between quantum computing and statistical learning is fundamental. Statistical methods like inference and estimation are key to understanding quantum phenomena. Quantum learning extends classical techniques by leveraging quantum features like superposition and entanglement, improving computational efficiency and performance. Neural networks have emerged as powerful models in machine and statistical learning due to their ability to capture complex relationships between variables. With the advent of quantum computing, a novel class of learning models, quantum neural networks (QNNs), has been proposed. These models harness quantum effects to enhance representational power, training efficiency, and optimization. However, understanding the theoretical foundations and practical advantages of QNNs remains an active area of research. In this work, we deploy newly developed ideas in QNNs to medical data analysis to show the possible advantages of such approaches on these data. For this purpose, we analyze the National Institute of Diabetes and Digestive and Kidney Diseases Diabetes dataset. Based on diagnostic measurements, the objective is to predict whether a patient has diabetes. We perform a comprehensive analysis of QNNs to identify the key elements of the architecture that most affect the performance in a classification task. Our approach involved testing many QNN configurations and systematically evaluating their performance. We tested the encoding techniques, the number of layers, the ansatz repetition scheme, and the loss functions among the different possible hyper-parameters. Results showed that appropriate encoding and loss functions significantly improve classification performance. While adding layers can enhance results, too many layers lead to diminishing returns. Further studies would help us better understand how these models perform in complex scenarios, such as multi-class classifications or unbalanced classification problems. In conclusion, the interplay between quantum computing and statistical science offers mutual benefits. On one side, statistical science provides essential tools and methodologies to analyze, interpret, and optimize quantum algorithms, facilitating a deeper understanding of quantum phenomena and improving computational efficiency. On the other, the computational capabilities of quantum computing have the potential to enable the resolution of complex problems and the development of novel statistical models.