  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.
