Quantum computations and quantum simulations with strings of trapped ions

The state-of-the-art of the Innsbruck trapped-ion quantum computer is reviewed. First, 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.

Finally, I will report on the experimental demonstration of both the digital and hybrid quantum-classical quantum 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 variationally solving optimization problems, using a feedback loop between a classical computer and a quantum co-processor, while benefiting from quantum resources.