Analysis of the shortest vector problems with quantum annealing to search the excited states

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