[论文解读] Towards Quantum Tensor Decomposition in Biomedical Applications

Myson Burch, Jiasen Zhang+13 more|ArXiv.org|Feb 18, 2025

Tensor decomposition and applications被引用 4

一句话总结

对生物医学中的张量分解进行全面综述，并探讨量子张量分解在近期量子设备上解决可扩展性和秩挑战的潜力。

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.

研究动机与目标

• 总结张量分解方法（CP、Tucker、TT、PARAFAC2、spiked、CANDELINC、DEDICOM、INDSCAL）及其在生物医学中的应用。
• 识别在处理大型生物医学数据集时，经典张量方法在可扩展性、秩确定与计算复杂性方面的挑战。
• 讨论量子算法在张量分解方面的最新进展，并在近容错设备上勾勒一个生物医学量子张量分解的框架。
• 提供实现量子增强张量分解在近端量子硬件上的资源估计与可行性讨论。

提出的方法

• 对张量分解层级（CP、Tucker、TT、PARAFAC2、spiked、CANDELINC、DEDICOM、INDSCAL）的调查与分类。
• 通过主题建模（BERTopic）对文献进行综述，以映射生物医学中的张量分解应用。
• 分析张量分解中的计算复杂性与相变（MMSE、信噪比、秩、稀疏性效应）。
• 讨论量子张量分解（QTD）的概念以及在近端量子设备上实现的框架。

实验结果

研究问题

• RQ1 在生物医学影像、多组学、空间转录组学中，最常使用哪些张量分解方法？
• RQ2 随着数据规模与复杂度增加，阻碍张量分解的主要可扩展性和秩确定挑战是什么？
• RQ3 如何利用量子计算改善生物医学中的张量分解，近端硬件是否具备可行性？
• RQ4 在具容错前的量子设备上实现量子增强张量分解的资源需求和可行性考虑有哪些？

主要发现

• 张量分解在医学影像、多组学和神经科学等领域广泛应用，影像领域为主导。
• 经典张量分解在数据规模与复杂度增加时，面临可扩展性和最优秩的挑战。
• 量子张量分解被探索为解决可扩展性潜在路径，并为近端设备提供初步框架。
• 本文提供初步的资源估计分析并讨论在近端量子硬件上实现QTD的可行性。