Quantum Branch-and-Bound Algorithm and its Application to the Travelling Salesman Problem

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...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 241; no. 2; pp. 168 - 184
Main Authors Markevich, E. A., Trushechkin, A. S.
Format Journal Article
LanguageEnglish
Published New York Springer US 09.08.2019
Springer
Springer Nature B.V
Subjects
ALGORITHMS
COMPARATIVE EVALUATIONS
EFFICIENCY
Management science
MATHEMATICAL METHODS AND COMPUTING
Mathematics
Mathematics and Statistics
Production scheduling
QUANTUM COMPUTERS
Search algorithms
Traveling salesman problem
quantum computer
quantum search
68Q12
81P68
quantum computing
travelling salesman problem
Grover’s algorithm
branch-and-bound method
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Summary: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.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04415-6