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Variational quantum multidimensional scaling algorithm

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Abstract

Quantum multidimensional scaling is a quantum dimensionality reduction algorithm. Its complex quantum circuit design structure and excessive qubits consumption make it difficult to run on the current quantum computers. In order to solve this problem, this paper proposes the variational quantum multidimensional scaling algorithm based on the variational quantum algorithm. Utilizing the parallel advantages of quantum computing to quickly compute low-dimensional embeddings of high-dimensional data, the variational quantum multidimensional scaling algorithm can provide lower time complexity; compared with the non-variational quantum multidimensional scaling algorithm, the variational quantum multidimensional scaling algorithm provides a simpler quantum circuit. In the noisy intermediate scale quantum era, the algorithm can run on a quantum computer. In addition, the article finally implemented the variational quantum multidimensional scaling algorithm on the Qiskit framework, proving the correctness of the algorithm.

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Data availability

The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This work is supported by the Beijing Natural Science Foundation No. 4212015.

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Authors and Affiliations

  1. Faculty of Information Technology, Beijing University of Technology, Chaoyang District, Beijing, 100124, China

    Xinglan Zhang, Feng Zhang, Yankun Guo & Fei Chen

  2. Beijing Key Laboratory of Trusted Computing, Chaoyang District, Beijing, 100124, China

    Xinglan Zhang, Feng Zhang, Yankun Guo & Fei Chen

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  1. Xinglan Zhang
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Correspondence to Feng Zhang.

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Zhang, X., Zhang, F., Guo, Y. et al. Variational quantum multidimensional scaling algorithm. Quantum Inf Process 23, 77 (2024). https://doi.org/10.1007/s11128-024-04289-x

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