To the identical parallel machine scheduling problems with sequence dependent setup times, a hybrid quantum-
inspired evolutionary programming(HQEP) is proposed. In HQEP, a Q-bit individual is defined to represent for a job
permutation. A Q-gate is introduced as a variation operator to drive the individuals toward better solutions. Improved
representation structures of individuals and mutation operator for scheduling problems are proposed. To evaluate the
effectiveness and convergence of the proposed method, experiments are carried out on different scales of randomly generated
test problems. Computational results show that HQEP outperforms evolutionary programming for scheduling, even with a
small population.