Quantum algorithm for preparing the ground state of a physical system through multi-step quantum resonant transitions

Abstract

We present a quantum algorithm for preparing the ground state of a physical system by using a multi-step quantum resonant transition (QRT) method. We construct a sequence of intermediate Hamiltonians to reach the system Hamiltonian, and then, starting from the ground state of an initial Hamiltonian, the system is sequentially evolved to the ground states of the intermediate Hamiltonians step by step using the QRT method, finally reaching the ground state of the system Hamiltonian. The algorithm can be run efficiently if the overlap between the ground states of any two adjacent Hamiltonians and the energy gap between the ground state and the first excited state of each Hamiltonian are not exponentially small. By using this algorithm, preparing the ground state of a system is transformed to simulating the time evolution of a sequence of time-independent Hamiltonians. This algorithm can also be used for calculating energy eigenvalues of a physical system.