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Quantum annealing is a heuristic algorithm for searching the ground state ofan Ising model. Heuristic algorithms aim to obtain near-optimal solutions witha reasonable computation time. Accordingly, many algorithms have so far beenproposed. In general, the performance of heuristic algorithms strongly dependson the instance of the combinatorial optimization problem to be solved becausethey escape the local minima in different ways. Therefore, combining severalalgorithms to exploit their complementary strength is effective for obtaininghighly accurate solutions for a wide range of combinatorial optimizationproblems. However, quantum annealing cannot be used to improve a candidatesolution obtained by other algorithms because it starts from an initial statewhere all spin configurations are found with a uniform probability. In thisstudy, we propose an Ising formulation of integer optimization problems toutilize quantum annealing in the iterative improvement strategy. Ourformulation exploits the biased sampling of degenerated ground states intransverse magnetic field quantum annealing. We also analytically show that afirst-order phase transition is successfully avoided for a fully connectedferromagnetic Potts model if the overlap between a ground state and a candidatesolution exceeds a threshold. The proposed formulation is applicable to a widerange of integer optimization problems and enables us to hybridize quantumannealing with other optimization algorithms.

Ising formulation of integer optimization problems for utilizing quantum annealing in iterative improvement strategy