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Frustration, or the competition between interacting components of a network,is often responsible for the complexity of many body systems, from social andneural networks to protein folding and magnetism. In quantum magnetic systems,frustration arises naturally from competing spin-spin interactions given by thegeometry of the spin lattice or by the presence of long-range antiferromagneticcouplings. Frustrated magnetism is a hallmark of poorly understood systems suchas quantum spin liquids, spin glasses and spin ices, whose ground states aremassively degenerate and can carry high degrees of quantum entanglement. Thecontrolled study of frustrated magnetism in materials is hampered by shortdynamical time scales and the presence of impurities, while numerical modelingis generally intractable when dealing with dynamics beyond N~30 particles.Alternatively, a quantum simulator can be exploited to directly engineerprescribed frustrated interactions between controlled quantum systems, andseveral small-scale experiments have moved in this direction. In this article,we perform a quantum simulation of a long-range antiferromagnetic quantum Isingmodel with a transverse field, on a crystal of up to N = 16 trapped Yb+ atoms.We directly control the amount of frustration by continuously tuning the rangeof interaction and directly measure spin correlation functions and theirdynamics through spatially-resolved spin detection. We find a pronounceddependence of the magnetic order on the amount of frustration, and extractsignatures of quantum coherence in the resulting phases.

Emergence and Frustration of Magnetic Order with Variable-Range Interactions in a Trapped Ion Quantum Simulator