Abstract
Quantum annealing can efficiently obtain solutions to combinatorial optimization problems. Size-reduction methods are used to treat large-scale combinatorial optimization problems that cannot be input directly into a quantum annealer because of its size limitation. Various size-reduction methods using fixing spins have been proposed as quantum-classical hybrid methods to obtain solutions. However, the high performance of these hybrid methods is yet to be clearly elucidated. In this study, we adopted a parameterized fixing spins method to verify the effects of fixing spins. The results revealed that setting the appropriate number of spins of the subproblem is crucial for obtaining a satisfactory solution, and the energy gap expansion is confirmed after fixing spins.