A milestone for a first generation quantum device would be to simulate complex dynamics beyond the capacity of a classical computer. This would involve mapping some model problem such an interacting two dimensional electron gas into a register of two state quantum systems (qubits), guiding the register by the appropriate control fields, and finally implementing a suitable measurement. For many systems of interest, the size and complexity of the model Hamiltonian prohibits an accurate analytic or computational treatment.

A quantum simulator could overcome such limitations because the interactions that the device is intended to emulate could be engineered into the device itself. We are interested in designing protocols for analogue and digital quantum simulators with focus on implementations in atomic/molecular and optical (AMO) systems. One promising approach is to use atoms or molecules trapped in an optical lattice which is a periodic potential produced by interfering standing waves of laser light. Such systems can simulate highly correlated spin lattice models with unknown properties using building blocks with well known physical properties. Possible constructions include platforms for quantum cellular automata and nearest neighbor spin lattice Hamiltonians in 1D, 2D, and 3D. A particularly compelling pursuit is the connection between protected quantum memory and topologically ordered spin states.