Quantum Higher Order Singular Value Decomposition

2019/08/02 by Lejia Gu, Gu, Lejia, Xiaoqiang Wang +5
Computer Science · Mathematics · #FOS: Physical sciences #Matrix Theory and Algorithms #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1908.00719

openalex publication_date 2019/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Higher order singular value decomposition (HOSVD) is an important tool for analyzing big data in multilinear algebra and machine learning. In this paper, we present two quantum algorithms for HOSVD. Our methods allow one to decompose a tensor into a core tensor containing tensor singular values and some unitary matrices by quantum computers. Compared to the classical HOSVD algorithm, our quantum algorithms provide an exponential speedup. Furthermore, we introduce a hybrid quantum-classical algorithm of HOSVD model applied in recommendation systems.

Citations

• Some Mathematical Notes on Three-Mode Factor Analysis
• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
• Tensor Decompositions and Applications
• Quantum Support Vector Machine for Big Data Classification
• Tensor Networks in a Nutshell
• Iterative Low-Rank Approximation for CNN Compression
• Quantum tensor singular value decomposition with applications to recommendation systems

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