Quantum Simulation of Spin Models on an Arbitrary Lattice with Trapped Ions

A collection of trapped atomic ions represents one of the most attractive
platforms for the quantum simulation of interacting spin networks and quantum
magnetism. Spin-dependent optical dipole forces applied to an ion crystal
create long-range effective spin-spin interactions and allow the simulation of
spin Hamiltonians that possess nontrivial phases and dynamics. Here we show how
appropriate design of laser fields can provide for arbitrary multidimensional
spin-spin interaction graphs even for the case of a linear spatial array of
ions. This scheme uses currently existing trap technology and is scalable to
levels where classical methods of simulation are intractable.