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.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 138, Quantum Computing, 2017.
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Markevich, E.A., Trushechkin, A.S. Quantum Branch-and-Bound Algorithm and its Application to the Travelling Salesman Problem. J Math Sci 241, 168–184 (2019). https://doi.org/10.1007/s10958-019-04415-6
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DOI: https://doi.org/10.1007/s10958-019-04415-6
Keywords and phrases
- quantum computing
- quantum computer
- quantum search
- Grover’s algorithm
- branch-and-bound method
- travelling salesman problem