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Quantum algorithm can achieve exponential speedup over its classical counterparts in solving some problems by considering their structures, e.g. the Abelian hidden subgroup problems (HSP). In this work, we apply a quantum algorithm of finding the ground state of a Hamiltonian via a multi-step quantum computation process (arxiv: 1912.06959) for solving some structured problems, where the solution to a problem is encoded in the ground state of the corresponding problem Hamiltonian. By decomposingarXiv:2204.03295v1 fatcat:wa7plrubhjbxfdqo3jrfadt5fe