The state-of-the-art of the Innsbruck trapped-ion quantum computer is briefly reviewed. We present an overview on the available quantum toolbox and discuss the scalability of the approach. Fidelities of quantum gate operations are evaluated and optimized by means of cycle- benchmarking  and we show the generation of a 16-qubit GHZ state. Entangled states of a fully controlled 20-ion string are investigated  and used for quantum simulations.
In the second part, we present both the digital quantum simulation and a hybrid quantum- classical simulation of the Lattice Schwinger model, a gauge theory of 1D quantum electrodynamics. Employing universal quantum computations, we investigate the dynamics of the pair-creation  and using a hybrid-classical ansatz, we determine steady-state properties of the Hamiltonian. Hybrid classical-quantum algorithms aim at solving optimization problems variationally, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources .
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Prof. Blatt is a world-renowned leading expert in trapped ion quantum computing/quantum simulations. His research centers on the areas of quantum optics and quantum information. He and his team were the first to teleport atoms, to create a "quantum byte" and a universal quantum simulator.