@Article{cmc.2020.010001,
AUTHOR = {Yue Ruan, Samuel Marsh, Xilin Xue, Zhihao Liu, Jingbo Wang},
TITLE = {The Quantum Approximate Algorithm for Solving Traveling  Salesman Problem},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {63},
YEAR = {2020},
NUMBER = {3},
PAGES = {1237--1247},
URL = {http://www.techscience.com/cmc/v63n3/38872},
ISSN = {1546-2226},
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, which decreases the search space 
significantly in comparison to other approaches. As a result, our method can achieve a 
higher probability for the shortest round-trip route with only half the number of qubits
consumed compared to IBM Q’s approach. We argue the formalization approach 
presented in this paper would lead to a generalized framework for finding, in the context 
of QAOA, high-quality approximate solutions to NP optimization problems.},
DOI = {10.32604/cmc.2020.010001}
}