Quantum algorithm for solving the hidden subgroup problems

In quantum computation, a problem can be solved by finding the ground state of the corresponding problem Hamiltonian that encodes the solution to the problem. We proposed a quantum algorithm for finding the ground state of a Hamiltonian via a multi-step quantum computation process (arxiv: 1912.06959), and applied the algorithm for efficiently solving a type of search problems with a special structure. In this work, we apply the algorithm for solving the hidden subgroup problems (HSP). We demonstrate that both the Abelian and the non-Abelian HSP can be reduced to the structured search problem, therefore can be solved efficiently in polynomial time by using our algorithm.Comment: 17 pages, 1 figur