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An Improved Noise Quantum Annealing Method for TSP

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Abstract

Traveling Salesman Problem (TSP) is a combinatorial optimization problem, which has NP-Complete (NPC) complexity. At present, there is no exact algorithm to solve similar problems, only an approximate algorithm to simplify the problem can be found. For example, quantum annealing algorithm (QA) can play such a role. QA transforms the distance matrix sum of TSP into Pauli matrix, adds a transverse magnetic field to realize the quantum tunneling effect, reduces the energy needed to cross the barrier, and reduces the number of iterations to find the optimal solution. However, although the QA has fewer iteration steps, it usually produces errors. In this context, this paper’s INQA improves the QA. In this paper, the theoretical basis of quantum annealing algorithm is introduced, aiming at the shortcomings of quantum annealing algorithm in solving TSP problem, a new algorithm INQA is proposed, and it is verified by experiments. In the case of high initial temperature, the INQA has larger search range and more active search. Meanwhile, with the decrease of temperature, the search range is reduced, and the accuracy of the algorithm is improved. In fact, QA in this paper is a quantum annealing method for simulation.

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  1. College of Computer and Information Science, Chongqing Normal University, Chongqing, China

    Yumin Dong & Zhijie Huang

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  1. Yumin Dong
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  2. Zhijie Huang
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Correspondence to Yumin Dong.

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Dong, Y., Huang, Z. An Improved Noise Quantum Annealing Method for TSP. Int J Theor Phys 59, 3737–3755 (2020). https://doi.org/10.1007/s10773-020-04628-5

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