Quantum Higher Order Singular Value Decomposition
Quantum Physics
2020-04-07 v2
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.
Cite
@article{arxiv.1908.00719,
title = {Quantum Higher Order Singular Value Decomposition},
author = {Lejia Gu and Xiaoqiang Wang and H. W. Joseph Lee and Guofeng Zhang},
journal= {arXiv preprint arXiv:1908.00719},
year = {2020}
}
Comments
14 pages; 6 figures; submitted for publication; comments are welcome!