Abstract: Method and apparatus for quantum simulation, based on a linear chain of ions. A gradient field is imposed to break the symmetry of the ion chain, and bichromatic driving fields are applied to bridge the energy gaps induced by the gradient field and thereby establish resonance couplings among the ions according to their relative positions in the gradient field. The combination of the gradient field and the bichromatic driving fields implement excitation hopping to simulate a variety of topologies according to higher¬dimensional Hamiltonians and boundary conditions, including ring, torus, Mobius strip configurations, as well as topologies with periodic boundary conditions. In particular synthetic gauge fields allow simulation of magnetic flux.