Liquid-state NMR simulations of quantum many-body problems

Recently developed quantum algorithms suggest that in principle, quantum computers can solve problems such as simulation of physical systems more efficiently than classical computers. Much remains to be done to implement these conceptual ideas into actual quantum computers. As a small-scale demonstration of their capability, we simulate a simple many-fermion problem, the Fano-Anderson model, using liquid-state nuclear magnetic resonance (NMR). We carefully designed our experiment so that the resource requirement would scale up polynomially with the size of the quantum system to be simulated. The experimental results obtained give us an insight to the quantum control required when simulating quantum systems with NMR techniques. The simulation of other physical systems, with different particle statistics, is also discussed.