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Quantum machine learning framework for longitudinal biomedical studies

Longitudinal biomedical studies play a vital role in tracking disease progression, treatment response, and the emergence of resistance mechanisms, particularly in complex disorders such as cancer and neurodegenerative diseases. However, the high dimensionality of biological data, combined with the limited size of longitudinal cohorts, presents significant challenges for traditional machine learning approaches. In this work, we explore the potential of quantum machine learning (QML) for longitudinal biomarker discovery. We propose a novel modification to the instantaneous quantum polynomial time (IQP) feature map, designed to encode temporal dependencies across multiple time points in biomedical datasets. Through numerical simulations on both synthetic and real-world datasets - including studies on follicular lymphoma and Alzheimer's disease - we demonstrate that our longitudinal IQP feature map improves the ability of quantum kernels to capture intra-subject temporal patterns, offering a promising direction for QML in clinical research.

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