Quantum algorithm for structured problems [article]

Hefeng Wang
2022 arXiv   pre-print
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 decomposing
more » ... the problem based on its structure, we construct a sequence of intermediate Hamiltonians to approach the problem Hamiltonian, and evolve the system through the ground states of the intermediate Hamiltonians via quantum resonant transitions sequentially, finally obtain the ground state of the problem Hamiltonian. We find that this algorithm achieves exponential speedup over classical algorithms in solving some structured problems, including problems that can be reduced to both the Abelian and the non-Abelian HSP. The HSP and the unstructured search problem can be casted in the same framework in this algorithm.
arXiv:2204.03295v1 fatcat:wa7plrubhjbxfdqo3jrfadt5fe