On Quantum Random Walks in Biomolecular Networks

Abstract: Biomolecular networks, such as protein-protein interactions, gene-gene associations, and cell-cell interactions, offer valuable insights into the complex organization of biological systems. These networks are key to understanding cellular functions, disease mechanisms, and identifying therapeutic targets. However, their analysis is challenged by the high dimensionality, heterogeneity, and sparsity of multi-omics data. Random walk algorithms are widely used to propagate information through disease modules, helping to identify disease-associated genes and uncover relevant biological pathways. In this work, we investigate the limitations of classical random walks and explore the potential of quantum random walks (QRWs) for biomolecular network analysis. We evaluate QRWs in two network-based applications. First, in a gene-gene interaction network associated with asthma, autism, and schizophrenia, QRWs more accurately rank disease-associated genes compared to classical methods. Second, in a structured multi-partite cell-cell interaction network derived from mouse brown adipose tissue, QRWs identify key driver genes in malignant cells that are overlooked by classical random walks. Our findings suggest that quantum random walks offer a promising alternative to classical approaches, with improved sensitivity to network structure and better performance in identifying biologically relevant features. This highlights their potential in advancing network medicine and systems biology.