  The shortest vector problem (SVP) is one of the lattice problems and is
mathematical basis for the lattice-based cryptography, which is expected to be
post-quantum cryptography. The SVP can be mapped onto the Ising problem, which
in principle can be solved by quantum annealing (QA). However, one issue in
solving the SVP using QA is that the solution of the SVP corresponds to the
first excited state of the problem Hamiltonian. Therefore, QA, which searches
for ground states, cannot provide a solution with high probability. In this
paper, we propose to adopt an excited-state search of the QA to solve the
shortest vector problem. We numerically show that the excited-state search
provides a solution with a higher probability than the ground-state search.
