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Quantum annealers are suited to solve several logistic optimization problemsexpressed in the QUBO formulation. However, the solutions proposed by thequantum annealers are generally not optimal, as thermal noise and otherdisturbing effects arise when the number of qubits involved in the calculationis too large. In order to deal with this issue, we propose the use of theclassical branch-and-bound algorithm, that divides the problem intosub-problems which are described by a lower number of qubits. We analyze theperformance of this method on two problems, the knapsack problem and thetraveling salesman problem. Our results show the advantages of this method,that balances the number of steps that the algorithm has to make with theamount of error in the solution found by the quantum hardware that the user iswilling to risk. All the results are actual runs on the quantum annealer D-WaveAdvantage.

Hybrid classical-quantum branch-and-bound algorithm for solving integer linear problems