Towards Quantum Tensor Decomposition in Biomedical Applications

2025-02-18

AI Summary

This work addresses two critical bottlenecks in tensor decomposition for multimodal biomedical data (e.g., medical imaging, multi-omics, spatial transcriptomics): poor scalability of latent representations and difficulty in determining optimal tensor rank. Through systematic topic modeling and comparative analysis, we identify fundamental limitations of classical decomposition methods—including Tucker, CP, and spike decomposition—in handling high-dimensional, heterogeneous biomedical tensors. To overcome these, we propose a quantum-enhanced tensor decomposition framework tailored for near-term quantum hardware, featuring novel quantum algorithm design, rigorous quantum resource estimation (qubit count and circuit depth), and a principled rank optimization strategy. We conduct the first feasibility assessment of this paradigm on real-world biomedical datasets, demonstrating its practical viability. Our contributions include a methodological blueprint and an implementable technical roadmap for quantum–biomedical integration, advancing both interpretable multimodal representation learning and quantum-aware computational biology.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Multi-modal Vision
• Data Mining & Knowledge Management: Mining of Visual, Multimedia & Multimodal Data

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Tensor decomposition in biomedical data
• Scalability and optimal rank challenges
• Quantum algorithms for tensor decomposition

Innovation

• Quantum tensor decomposition methods
• Topic modeling-based literature analysis
• Quantum computing feasibility analysis