In this talk, the basic toolbox of the Innsbruck quantum computer based on strings of trapped Ca+ ions will be reviewed [1] and an overview will be given on our current experiments in the field of quantum information 
science.
For quantum information processing, the toolbox operations are used to encode one logical qubit in entangled states distributed over seven trapped-ion qubits. We demonstrate the capability of the code to detect one bit flip, phase flip or a combined error of both, regardless on which of the qubits they occur.
Furthermore, we apply combinations of the entire set of logical single-qubit Clifford gates on the encoded qubit to explore its computational capabilities [2].
With the quantum toolbox both analog and digital quantum simulations are carried out [3].
The basic simulation procedure will be presented and its application will be discussed for a variety of spin Hamiltonians.
Including a carefully controlled dissipation mechanism, the toolbox even allows for the quantum simulation of open systems [4].
With long ion strings, the quantum toolbox is applied to investigate the propagation of entanglement in a quantum many-body system represented by the trapped-ion qubits [5].
[1] P. Schindler et al., New. J. Phys. 15, 123012 (2013).
[2] D. Nigg, M. Müller et al., Science 345, 302 (2014).
[3] R. Blatt and C. F. Roos, Nature Phys. 8, 277 (2012).
[4] J. T. Barreiro et al., Nature 470, 486 (2011).
[5] P. Jurcevic, et al., Nature 511, 202 (2014).
Prof. Rainer Blatt – Institute for Experimental Physics – University of Innsbruck – Institute for Quantum Optics and Quantum Information – Austrian Academy of Sciences.
