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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Vydáno v:	Entropy (Basel, Switzerland) Ročník 26; číslo 4; s. 345
Hlavní autoři:	Sanavio, Claudio, Tignone, Edoardo, Ercolessi, Elisa
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Switzerland MDPI AG 01.04.2024
Témata:	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
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Abstract	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.
AbstractList	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.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. 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.
Audience	Academic
Author	Tignone, Edoardo Sanavio, Claudio Ercolessi, Elisa
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Cites_doi	10.1103/PhysRevE.58.5355 10.1007/s10589-016-9844-y 10.1126/science.aaa4170 10.1088/1742-6596/143/1/012002 10.1007/BF01720015 10.3389/fphy.2014.00005 10.1103/RevModPhys.90.015002 10.1088/1751-8121/41/20/209801 10.1103/PhysRevB.82.024511 10.1143/JPSJ.5.435 10.2307/1910129 10.1137/1.9780898718515 10.1103/PhysRevA.92.052323 10.1287/mnsc.13.9.723
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SubjectTerms	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
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Title	Hybrid Classical–Quantum Branch-and-Bound Algorithm for Solving Integer Linear Problems
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