# 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.

## 4 Citations

Quantum tensor singular value decomposition with applications to recommendation systems

- Computer ScienceArXiv
- 2019

It can be proved that the quantum version of the t-svd for a third-order tensor $\mathcal{A} \in \mathbb{R}^{N\times N \times N}$ achieves the complexity of $O(N{\rm polylog}(N)$, an exponential speedup compared with its classical counterpart.

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.

- Computer ScienceJournal of Physics Communications
- 2021

This paper proves that the quantum t-svd algorithm for a third-order N dimensional tensor runs in time Npolylog(N) if the authors do not recover classical information from the quantum output state, thus achieving low time complexity.

Quantum Algorithms for Data Representation and Analysis

- Computer ScienceArXiv
- 2021

We narrow the gap between previous literature on quantum linear algebra and useful data analysis on a quantum computer, providing quantum procedures that speed-up the solution of eigenproblems for…

Quantum Machine Learning Algorithm for Knowledge Graphs

- Computer ScienceACM Transactions on Quantum Computing
- 2021

This paper proposes the first quantum machine learning algorithm for making inference on tensorized data, e.g., on knowledge graphs, and achieves exponential speedup with a runtime that is polylogarithmic in the dimension of knowledge graph tensor.

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Quantum tensor singular value decomposition with applications to recommendation systems

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It can be proved that the quantum version of the t-svd for a third-order tensor $\mathcal{A} \in \mathbb{R}^{N\times N \times N}$ achieves the complexity of $O(N{\rm polylog}(N)$, an exponential speedup compared with its classical counterpart.

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