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Topological Quantum Computation with Trapped Ions


Arbitrarily long quantum computation requires techniques to overcome errors accumulated during the operation.  Here, different approaches have been proposed, with topological quantum computation yielding one of the highest thresholds against errors.  In this talk I will first provide a brief introduction into topological quantum computation, in particular the color code.  Subsequently I will show how, for the first time, a qubit has been topologically encoded using an ion-trap based quantum computer.  The presented experimental data illustrates how we can detect all physical single-qubit errors, perform the entire set of Clifford operations on this logical qubit and investigate its coherence
properties.  The presentation is concluded by an outline on upcoming milestones and their experimental as well as theoretical challenges.