Spiking neural network dynamic system modeling for computation of quantum annealing and its convergence analysis

Abstract

Quantum annealing algorithm is a classical natural computing method for skeuomorphs, and its algorithm design and application research have achieved fruitful results, so it is widely integrated into the research of modern intelligent optimization algorithm. This paper attempts to use the spiking neural network (SNN) dynamic system model to simulate the operation mechanism and convergence of the quantum annealing algorithm, and compares the process of searching the optimal solution to the elastic motion in the quantum tunneling field, and the change of function value during the operation of the algorithm is the simple harmonic vibration or damped vibration of quantum. Spiking neural network dynamic system model simulates the human brain by incorporating synaptic state and time components into their operational models, which represents the process of quantum fluctuations. The local convergence in the early stage and the global convergence in the late stage of the algorithm are proved by using the qualitative theory of ordinary differential equations to solve and analyze the dynamic system model, and a reasonable theoretical explanation is given for its operation mechanism. Several typical test problems are selected for experimental verification. The experimental results show that the numerical convergence curve is consistent with the convergence conclusion of theoretical analysis. Finally, both theoretical and experimental analyses show that the SNN dynamic system model established in this paper is suitable to describe the quantum annealing algorithm for optimization.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Key Program) under Grant 61836010. The authors would like to thank their laboratory team member’s assistance.

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Correspondence to Chenhui Zhao or Donghui Guo.

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Zhao, C., Huang, Z. & Guo, D. Spiking neural network dynamic system modeling for computation of quantum annealing and its convergence analysis. Quantum Inf Process 20, 70 (2021). https://doi.org/10.1007/s11128-021-03003-5

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Keywords

  • Convergence stability
  • Spiking neural network (SNN) model
  • Quantum annealing (QA)
  • Local convergence
  • Global convergence