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    The Quantum Approximate Algorithm for Solving Traveling Salesman Problem

    Yue Ruan1, *, Samuel Marsh2, Xilin Xue1, Zhihao Liu3, Jingbo Wang2, *

    CMC-Computers, Materials & Continua, Vol.63, No.3, pp. 1237-1247, 2020, DOI:10.32604/cmc.2020.010001

    Abstract The Quantum Approximate Optimization Algorithm (QAOA) is an algorithmic framework for finding approximate solutions to combinatorial optimization problems. It consists of interleaved unitary transformations induced by two operators labelled the mixing and problem Hamiltonians. To fit this framework, one needs to transform the original problem into a suitable form and embed it into these two Hamiltonians. In this paper, for the well-known NP-hard Traveling Salesman Problem (TSP), we encode its constraints into the mixing Hamiltonian rather than the conventional approach of adding penalty terms to the problem Hamiltonian. Moreover, we map edges (routes) connecting each pair of cities to qubits,… More >

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