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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2017, Volume 138, Pages 60–75 (Mi into214)  

Quantum branch-and-bound algorithm and its application to the travelling salesman problem

E. A. Markevicha, A. S. Trushechkinbac

a National Engineering Physics Institute "MEPhI", Moscow
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
c National University of Science and Technology «MISIS»

Abstract: 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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation МК-2815.2017.1
This work was supported by the Grant of the President of the Russian Federation (project MK-2815.2017.1).


Full text: PDF file (261 kB)

Bibliographic databases:

Document Type: Article
UDC: 517.958:530.145, 519.85
MSC: 81P68, 68Q12

Citation: E. A. Markevich, A. S. Trushechkin, “Quantum branch-and-bound algorithm and its application to the travelling salesman problem”, Quantum computing, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 138, VINITI, Moscow, 2017, 60–75

Citation in format AMSBIB
\Bibitem{MarTru17}
\by E.~A.~Markevich, A.~S.~Trushechkin
\paper Quantum branch-and-bound algorithm and its application to the travelling salesman problem
\inbook Quantum computing
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 138
\pages 60--75
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into214}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3801251}


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