# Towards Quantum Tensor Decomposition in Biomedical Applications

arXiv: https://arxiv.org/abs/2502.13140 · HTML: https://mlsanity.com/paper/2502.13140/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 141 references that are in the map.
- First posted on arXiv 18 Feb 2025.

## Builds on (most cited first, 21 of 21)

- [BERTopic: Neural topic modeling with a class-based TF-IDF procedure](https://mlsanity.com/paper/2203.05794/) (2022)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [A statistical model for tensor PCA](https://mlsanity.com/paper/1411.1076/) (2014)
- [Introduction to Tensor Decompositions and their Applications in Machine Learning](https://mlsanity.com/paper/1711.10781/) (2017)
- [Tensor Clustering with Planted Structures: Statistical Optimality and Computational Limits](https://mlsanity.com/paper/2005.10743/) (2020)
- [Learning from Binary Multiway Data: Probabilistic Tensor Decomposition and its Statistical Optimality](https://mlsanity.com/paper/1811.05076/) (2018)
- [Tensor Decomposition for Model Reduction in Neural Networks: A Review](https://mlsanity.com/paper/2304.13539/) (2023)
- [Hyperspectral Super-Resolution with Coupled Tucker Approximation: Recoverability and SVD-based algorithms](https://mlsanity.com/paper/1811.11091/) (2018)
- [Variational Quantum Singular Value Decomposition](https://mlsanity.com/paper/2006.02336/) (2020)
- [Characterizing Spatiotemporal Transcriptome of Human Brain via Low Rank Tensor Decomposition](https://mlsanity.com/paper/1702.07449/) (2017)
- [Quantum Computing at the Frontiers of Biological Sciences](https://mlsanity.com/paper/1911.07127/) (2019)
- [Average-Case Complexity of Tensor Decomposition for Low-Degree Polynomials](https://mlsanity.com/paper/2211.05274/) (2022)
- [Classical and Quantum Algorithms for Tensor Principal Component Analysis](https://mlsanity.com/paper/1907.12724/) (2019)
- [Hybrid quantum-classical graph neural networks for tumor classification in digital pathology](https://mlsanity.com/paper/2310.11353/) (2023)
- [Tensor Analysis and Fusion of Multimodal Brain Images](https://mlsanity.com/paper/1506.06040/) (2015)
- [Multi-Slice Low-Rank Tensor Decomposition Based Multi-Atlas Segmentation: Application to Automatic Pathological Liver CT Segmentation](https://mlsanity.com/paper/2102.12056/) (2021)
- [A Tensor Factorization Method for 3D Super-Resolution with Application to Dental CT](https://mlsanity.com/paper/1807.10027/) (2018)
- [Single Image Super-Resolution of Noisy 3D Dental CT Images Using Tucker Decomposition](https://mlsanity.com/paper/2009.08657/) (2020)
- [Statistical Estimation in the Spiked Tensor Model via the Quantum Approximate Optimization Algorithm](https://mlsanity.com/paper/2402.19456/) (2024)
- [Post-Training Network Compression for 3D Medical Image Segmentation: Reducing Computational Efforts via Tucker Decomposition](https://mlsanity.com/paper/2404.09683/) (2024)

## Built on by (most cited first, 2 of 2)

- [Quantum Machine Learning in Precision Medicine and Drug Discovery -- A Game Changer for Tailored Treatments?](https://mlsanity.com/paper/2502.18639/) (2025)
- [Structured 3D-SVD: A Practical Framework for the Compression and Reconstruction of Biological Volumetric Images](https://mlsanity.com/paper/2604.16947/) (2026)

## Abstract (arXiv)

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.