Hybrid Classical–Quantum Branch-and-Bound Algorithm for Solving Integer Linear Problems

Quantum annealers are suited to solve several logistic optimization problems expressed in the QUBO formulation. However, the solutions proposed by the quantum annealers are generally not optimal, as thermal noise and other disturbing effects arise when the number of qubits involved in the calculatio...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Vol. 26; no. 4; p. 345
Main Authors: Sanavio, Claudio, Tignone, Edoardo, Ercolessi, Elisa
Format: Journal Article
Language:English
Published: Switzerland MDPI AG 01.04.2024
Subjects:
Algorithms
Annealing
binary linear problem
branch and bound
Hardware
Knapsack problem
Management science
Optimization
quantum annealing
Quantum computing
Qubits (quantum computing)
Thermal noise
Traveling salesman problem
Variables
branch and bound
knapsack problem
traveling salesman problem
quantum annealing
binary linear problem
ISSN:1099-4300, 1099-4300
Online Access:Get full text
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Summary:Quantum annealers are suited to solve several logistic optimization problems expressed in the QUBO formulation. However, the solutions proposed by the quantum annealers are generally not optimal, as thermal noise and other disturbing effects arise when the number of qubits involved in the calculation is too large. In order to deal with this issue, we propose the use of the classical branch-and-bound algorithm, that divides the problem into sub-problems which are described by a lower number of qubits. We analyze the performance of this method on two problems, the knapsack problem and the traveling salesman problem. Our results show the advantages of this method, that balances the number of steps that the algorithm has to make with the amount of error in the solution found by the quantum hardware that the user is willing to risk. The results are obtained using the commercially available quantum hardware D-Wave Advantage, and they outline the strategy for a practical application of the quantum annealers.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e26040345