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Born machine model based on matrix product state quantum circuit

Author

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  • Gong, Li-Hua
  • Xiang, Ling-Zhi
  • Liu, Si-Hang
  • Zhou, Nan-Run

Abstract

Born machine model based on the probability interpretation of the wave function combining quantum information theory with machine learning method provides a new tool to study the generative models. The Born machine model with a general parameterized quantum circuit generally requires the same number of qubits as the sample feature size of the dataset to be processed, while each sample usually contains thousands of features in actual dataset. A novel Born machine model with a matrix product state quantum circuit is proposed, which requires less qubits than that with a general parameterized quantum circuit, so it can make better use of scarce qubit resources in near-term quantum devices. And the presented Born machine model is trained with the maximal mean discrepancy loss function. The learning process of the proposed Born machine model is numerically simulated on the Bars-and-Stripes dataset. The simulation results verify the feasibility of the Born machine model with the matrix product state quantum circuit.

Suggested Citation

  • Gong, Li-Hua & Xiang, Ling-Zhi & Liu, Si-Hang & Zhou, Nan-Run, 2022. "Born machine model based on matrix product state quantum circuit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    • Handle: RePEc:eee:phsmap:v:593:y:2022:i:c:s0378437122000322
    DOI: 10.1016/j.physa.2022.126907
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    References listed on IDEAS

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    1. Jacob Biamonte & Peter Wittek & Nicola Pancotti & Patrick Rebentrost & Nathan Wiebe & Seth Lloyd, 2017. "Quantum machine learning," Nature, Nature, vol. 549(7671), pages 195-202, September.
    2. Anderson, N. H. & Hall, P. & Titterington, D. M., 1994. "Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 41-54, July.
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    Cited by:

    1. Wu, Chenyi & Huang, Fei & Dai, Jingyi & Zhou, Nanrun, 2022. "Quantum SUSAN edge detection based on double chains quantum genetic algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    2. Zeng, Qing-Wei & Ge, Hong-Ying & Gong, Chen & Zhou, Nan-Run, 2023. "Conditional quantum circuit Born machine based on a hybrid quantum–classical​ framework," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).

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