Abstract: Trapped strings of cold ions provide an ideal system for quantum information processing. The quantum information can be stored in individual ions and these qubits can be individually prepared; the corresponding quantum states can be manipulated and measured with nearly 100% detection efficiency. With a small ion-trap quantum computer based on up to eight trapped Ca+ ions as qubits we have generated genuine quantum states in a pre-programmed way. In particular, we have generated GHZ and W states in a fast and scalable way and we have demonstrated for the first time a Toffoli gate with trapped ions which is analyzed via state and process tomography. High fidelity CNOT-gate operations are investigated towards fault-tolerant quantum computing and using logical qubits encoded in decoherence-free subspaces, a universal set of gate operations was implemented and analyzed. As applications of quantum information processing, an experimental state-independent test of quantum contextuality was performed, a simulation of the Dirac equation was implemented and a quantum walk with a trapped ion was realized.
This work is supported by the Austrian Science Fund (FWF), by the European Commission (CONQUEST, SCALA) and in parts by IARPA.