Quantum simulation of spin models can provide insights into a variety of hard problems, including the competition between entanglement and decoherence in open quantum systems. Trapped ions are an established platform for quantum simulation, but only systems with fewer than 20 ions have demonstrated quantum correlations. We benchmark non-equilibrium, quantum spin dynamics arising from an engineered Ising interaction in two-dimensional arrays of up to 230 9Be+ ions in a Penning trap. We verify entanglement at early times by measuring spin squeezing. At later timeswhere spin-squeezing is not a useful entanglement witness we measure the full counting statistics of the non-Gaussian spin state. We find good agreement with ab-initio theory that includes decoherence. This quantum simulation of 2D Ising interactions with full connectivity demonstrates a key component of other spin models, such as the transverse-field Ising model with variable range interactions, in which controlled numerical solutions are classically intractable.
Pub Type: Journals
entanglement, Ising model, non-equilibrium dynamics, Penning ion trap, quantum magnetism, quantum simulation, transverse-field Ising model