Quantum Higher Order Singular Value Decomposition

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.

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