  The demand for classical-quantum hybrid algorithms to solve large-scale
combinatorial optimization problems using quantum annealing (QA) has increased.
One approach involves obtaining an approximate solution using classical
algorithms and refining it using QA. In previous studies, such variables were
determined using molecular dynamics (MD) as a continuous optimization method.
We propose a method that uses the simple continuous relaxation technique called
linear programming (LP) relaxation. Our method demonstrated superiority through
comparative experiments with the minimum vertex cover problem versus the
previous MD-based approach. Furthermore, the hybrid approach of LP relaxation
and simulated annealing showed advantages in accuracy and speed compared to
solving with simulated annealing alone.
