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Quantum Higher Order Singular Value Decomposition
Lejia Gu, Xiaoqiang Wang, Guofeng Zhang·August 2, 2019·DOI: 10.1109/SMC.2019.8914525
Computer ScienceMathematicsPhysics
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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 a quantum algorithm for higher order singular value decomposition. Our method allows 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 algorithm provides an exponential speedup.