Multi-qubit gates mediated by several strongly coupled motional modes

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Goal of this project is to devise quantum gates for more than two qubits outside the Lamb-Dicke regime that are mediated by several motional modes. Since the coupling between an individual ion and a single motional mode decreases with the number of ions in the same potential well, even a moderate number of ions implies a substantial increase of gate time. The rst task of this project will be to extend existing schemes for entangling gates using several motional modes to make them applicable to entangling interactions outside the Lamb-Dicke regime. Since the different motional modes will show un-harmonicities and there will be un-harmonic interactions between different modes, such extensions will require suitably designed driving proles.The second task of the project will be the design of dedicated gate operations for more than two trapped ions. Whereas common gate schemes realise an overall set of pairwise entangling interactions for any number of trapped ions, the realisation of a desired gate of several qubits typically requires a full series of elementary ealisable gates. We will focus on the directly realisati of multi-qubit gates such as the Toffoli gate as well as effective tree-body and four body interactions between ions. The former goal would help to reduce the gate count of quantum algorithms; the latter goal would provide a tool-box for quantum simulation and it would help to realise topological protection of quantum information.