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It is difficult to calculate the energy levels and eigenstates of a largephysical system on a classical computer because of the exponentially growingsize of the Hilbert space. In this work, we experimentally demonstrate aquantum algorithm which could solve this problem via simulated resonanttransitions. Using a four-qubit quantum simulator in which two qubits are usedas ancillas for control and measurement, we obtain the energy spectrum of a2-qubit low-energy effective Hamiltonian of the water molecule. The simulatedtransitions allow the state of the quantum simulator to transform and accesslarge regions of the Hilbert space, including states that have no overlap withthe initial state. Furthermore, we make use of this algorithm to efficientlyprepare specific eigenstates on the simulator according to the measuredeigenenergies.

Quantum Simulation of Resonant Transitions for Solving the Eigen-problem of an Effective Water Hamiltonian