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A quantum approximate optimization algorithm for solving Hamilton path problem

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Abstract

In recent years, combinatorial optimization has been widely studied. The existing optimization solutions are prone to fall into local optimal solutions and have a lower probability of obtaining global optimal solutions. Quantum approximate optimization algorithm (QAOA) is an effective algorithm that can obtain the optimal solution with high probability. In this paper, the problem Hamiltonian is obtained by summing the problem function and the deformed constraints. Through theoretical formula derivation, the problem Hamiltonian is transformed into the Ising model. The performance of the experimental result under different optimizers and asynchronous lengths is verified on pyQPanda. The experimental results show that when using the problem Hamiltonian method set in this paper, the probability of obtaining the optimal solution is 99.59%. Compared with other methods, the proposed method can alleviate the risk of falling into local optimal solutions and obtain the global optimal solution with a higher probability.

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Acknowledgements

This work was funded in part by the Liaoning Provincial Department of Education Research under Grant LJKZ0208, in part by the Scientific Research Foundation for Advanced Talents from Shenyang Aerospace University under Grant 18YB06, and National Basic Research Program of China under Grant JCKY2018410C004.

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  1. School of Computer Science, Shenyang Aerospace University, Daoyi Nan Street, Shenyang, 110136, Liaoning, China

    Changqing Gong, Ting Wang, Wanying He & Han Qi

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  1. Changqing Gong
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  2. Ting Wang
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  3. Wanying He
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  4. Han Qi
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Correspondence to Han Qi.

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Gong, C., Wang, T., He, W. et al. A quantum approximate optimization algorithm for solving Hamilton path problem. J Supercomput 78, 15381–15403 (2022). https://doi.org/10.1007/s11227-022-04462-y

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  • DOI: https://doi.org/10.1007/s11227-022-04462-y

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