Quantum simulation of spin models on an arbitrary lattice with trapped ions

Abstract

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