Geodesic
Quantum branch-and-bound algorithm and its application to the travelling salesman problem
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Quantum computing, Tome 138 (2017), pp. 60-75.

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We propose a quantum branch-and-bound algorithm based on the general scheme of the branch-and-bound method and the quantum nested searching algorithm and examine its computational efficiency. We also compare this algorithm with a similar classical algorithm on the example of the travelling salesman problem. We show that in the vast majority of problems, the classical algorithm is quicker than the quantum algorithm due to greater adaptability. However, the operation time of the quantum algorithm is constant for all problem, whereas the classical algorithm runs very slowly for certain problems. In the worst case, the quantum branch-and-bound algorithm is proved to be several times more efficient than the classical algorithm.
Keywords: quantum computing, quantum computer, quantum search, Grover's algorithm, branch-and-bound method, travelling salesman problem. 
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     author = {E. A. Markevich and A. S. Trushechkin},
     title = {Quantum branch-and-bound algorithm and its application  to the travelling salesman problem},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {60--75},
     publisher = {mathdoc},
     volume = {138},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_138_a4/}
}
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E. A. Markevich; A. S. Trushechkin. Quantum branch-and-bound algorithm and its application  to the travelling salesman problem. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Quantum computing, Tome 138 (2017), pp. 60-75. http://geodesic.mathdoc.fr/item/INTO_2017_138_a4/