  Quantum annealing (QA) is a promising approach for not only solving
combinatorial optimization problems but also simulating quantum many-body
systems such as those in condensed matter physics. However, non-adiabatic
transitions constitute a key challenge in QA. The choice of the drive
Hamiltonian is known to affect the performance of QA because of the possible
suppression of non-adiabatic transitions. Here, we propose the use of a drive
Hamiltonian that preserves the symmetry of the problem Hamiltonian for more
efficient QA. Owing to our choice of the drive Hamiltonian, the solution is
searched in an appropriate symmetric subspace during QA. As non-adiabatic
transitions occur only inside the specific subspace, our approach can
potentially suppress unwanted non-adiabatic transitions. To evaluate the
performance of our scheme, we employ the XY model as the drive Hamiltonian in
order to find the ground state of problem Hamiltonians that commute with the
total magnetization along the $z$ axis. We find that our scheme outperforms the
conventional scheme in terms of the fidelity between the target ground state
and the states after QA.
