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001020504 1001_ $$0P:(DE-Juel1)194305$$aMontanez-Barrera, Jhon Alejandro$$b0$$eCorresponding author$$ufzj
001020504 1112_ $$a2023 IEEE International Conference on Quantum Computing and Engineering (QCE)$$cBellevue, WA$$d2023-09-17 - 2023-09-22$$wUSA
001020504 245__ $$aImproving Performance in Combinatorial Optimization Problems with Inequality Constraints: An Evaluation of the Unbalanced Penalization Method on D-Wave Advantage
001020504 260__ $$c2023
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001020504 520__ $$aCombinatorial optimization problems are one ofthe target applications of current quantum technology, mainly because of their industrial relevance, the difficulty of solving large instances of them classically, and their equivalence to Ising Hamiltonians using the quadratic unconstrained binary optimization (QUBO) formulation. Many of these applications have inequality constraints, usually encoded as penalization terms in the QUBO formulation using additional variables known as slack variables. The slack variables have two disadvantages: (i) these variables extend the search space of optimal and suboptimal solutions, and (ii) the variables add extra qubits and connections to the quantum algorithm. Recently, a new method known as unbalanced penalization has been presented to avoid using slack variables. This method offers a trade-off between additional slack variables to ensure that the optimal solution is given by the ground state of the Ising Hamiltonian, and using an unbalanced heuristic function to penalize the region where the inequality constraint is violated with the only certainty that the optimal solution will be in the vicinity of the ground state. This work tests the unbalanced penalization method using real quantum hardware on D-Wave Advantage for the traveling salesman problem (TSP). The results show that the unbalanced penalization method outperforms the solutions found using slack variables and sets a new record for the largest TSP solved with quantum
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001020504 7001_ $$0P:(DE-HGF)0$$avan den Heuvel, Pim$$b1
001020504 7001_ $$0P:(DE-Juel1)167542$$aWillsch, Dennis$$b2$$ufzj
001020504 7001_ $$0P:(DE-Juel1)138295$$aMichielsen, Kristel$$b3$$ufzj
001020504 773__ $$a10.1109/QCE57702.2023.00067
001020504 8564_ $$uhttps://ieeexplore.ieee.org/document/10313601/
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