Towards Quantum Tensor Decomposition in Biomedical Applications

Myson Burch; Jiasen Zhang; Gideon Idumah; Hakan Doga; Richard Lartey; Lamis Yehia; Mingrui Yang; Murat Yildirim; Mihriban Karaayvaz; Omar Shehab; Weihong Guo; Ying Ni; Laxmi Parida; Xiaojuan Li; Aritra Bose

arXiv · 2502.13140

Towards Quantum Tensor Decomposition in Biomedical Applications

Myson Burch·Jiasen Zhang·Gideon Idumah·Hakan Doga·Richard Lartey·Lamis Yehia·Mingrui Yang·Murat Yildirim·Mihriban Karaayvaz·Omar Shehab·Weihong Guo·Ying Ni·Laxmi Parida·Xiaojuan Li·Aritra Bose

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Abstract

Tensor decomposition has emerged as a powerful framework for feature extraction in multi-modal biomedical data. In this review, we present a comprehensive analysis of tensor decomposition methods such as Tucker, CANDECOMP/PARAFAC, spiked tensor decomposition, etc. and their diverse applications across biomedical domains such as imaging, multi-omics, and spatial transcriptomics. To systematically investigate the literature, we applied a topic modeling-based approach that identifies and groups distinct thematic sub-areas in biomedicine where tensor decomposition has been used, thereby revealing key trends and research directions. We evaluated challenges related to the scalability of latent spaces along with obtaining the optimal rank of the tensor, which often hinder the extraction of meaningful features from increasingly large and complex datasets. Additionally, we discuss recent advances in quantum algorithms for tensor decomposition, exploring how quantum computing can be leveraged to address these challenges. Our study includes a preliminary resource estimation analysis for quantum computing platforms and examines the feasibility of implementing quantum-enhanced tensor decomposition methods on near-term quantum devices. Collectively, this review not only synthesizes current applications and challenges of tensor decomposition in biomedical analyses but also outlines promising quantum computing strategies to enhance its impact on deriving actionable insights from complex biomedical data.

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Myson Burch, Jiasen Zhang, Gideon Idumah, Hakan Doga, Richard Lartey, Lamis Yehia, Mingrui Yang, Murat Yildirim, Mihriban Karaayvaz, Omar Shehab, Weihong Guo, Ying Ni, Laxmi Parida, Xiaojuan Li, Aritra Bose. 2025-02-18. Towards Quantum Tensor Decomposition in Biomedical Applications. https://arxiv.org/abs/2502.13140

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