  It is exponentially hard to simulate quantum systems by classical algorithms,
while quantum computer could in principle solve this problem polynomially. We
demonstrate such an quantum-simulation algorithm on our NMR system to simulate
an hydrogen molecule and calculate its ground-state energy. We utilize the NMR
interferometry method to measure the phase shift and iterate the process to get
a high precision. Finally we get 17 precise bits of the energy value, and we
also analyze the source of the error in the simulation.
