Quantum Higher Order Singular Value Decomposition

@article{Gu2019QuantumHO,
  title={Quantum Higher Order Singular Value Decomposition},
  author={Lejia Gu and Xiaoqiang Wang and Guofeng Zhang},
  journal={2019 IEEE International Conference on Systems, Man and Cybernetics (SMC)},
  year={2019},
  pages={1166-1171}
}
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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Quantum tensor singular value decomposition* * This research is supported in part by Hong Kong Research Grant council (RGC) grants (No. 15208418, No. 15203619, No. 15506619) and Shenzhen Fundamental Research Fund, China under Grant No. JCYJ20190813165207290.
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