Precise and efficient characterization of entangled multi-qubit quantum states and quantum gates with trapped ions

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Quantum physics and particularly entanglement may serve for secure communication, precise measurements, efficient simulations of physical systems and fast quantum algorithms. Furthermore, entanglement is an intriguing phenomenon, since it discriminates the quantum world from the classical world. To date the most successful physical system for investigating entanglement are trapped atomic ions. In this project we develop methods to experimentally detect and characterize multi-particle entangled quantum states and multi-particle quantum gates in a close cooperation between theory and experiment. These methods will be applied to investigate multipartite entangled states and multi-qubit quantum gates realized using magnetic gradient induced coupling (MAGIC) between trapped atomic ions. MAGIC creates long range coupling between multiple ions. It allows for the realization of multi-qubit quantum gates using radio frequency radiation and does not require cooling trapped ions to their motional ground state. For the experimental realization of quantum information it is crucial to reproducibly carry out state preparation, state manipulation (quantum gates), and state detection with high accuracy. However, the efficient characterization of quantum states and gates is still challenging because most of the methods require prohibitively large resources for many-particle states or are only applicable to special cases. We will investigate how systematic and statistical errors affect experimental quantum gates and will develop efficient tools to characterize the performance of such gates. Toffoli gates, universal building blocks for quantum algorithms, will be experimentally implemented taking advantage of multi-qubit coupling based on MAGIC and will be characterized employing these novel methods. In addition, we will develop new entanglement criteria that can be applied efficiently in an experiment. They will be used to experimentally detect and characterize entangled weighted graph states of N trapped ions (with N between 3 and 9) that will be realized for the first time. Furthermore, state selective detection of hyperfine qubits will be investigated. First the complete detection process will be described exactly and then it will be numerically simulated. Finally it will be improved in close interaction between theory and experiment to obtain the highest possible detection fidelity. The insight gained in this project will be applicable to numerous other experiments in quantum information science encompassing many other physical systems.