Multi-qubit gates mediated by several strongly coupled motional modes

这个项目的目标是为Lamb-Dicke机制之外的两个以上的量子比特设计量子门，这些量子比特由几种运动模式介导。由于单个离子与单个运动模间的耦合随着相同势垒中的离子数目的增加而减小，因此即使是中等数目的离子也意味着栅极时间的显著增加。这个项目的第一个任务将是扩展现有的使用几种运动模式的纠缠门方案，使它们适用于Lamb-Dicke机制之外的纠缠相互作用。由于不同的运动模式会表现出非谐和，不同的模式之间会存在非谐和的相互作用，这样的扩展将需要适当设计的驱动栅极。该项目的第二个任务将是为两个以上的囚禁离子设计专用的门操作。虽然普通的门方案实现了任何数量的囚禁离子的一整套成对纠缠相互作用，但要实现所需的几个量子比特的门通常需要一系列基本的可实现的门。我们将专注于多量子比特门的直接实现，如Toffoli门以及离子之间有效的树体和四体相互作用。前一个目标将有助于减少量子算法的门数；后一个目标将为量子模拟提供工具箱，并有助于实现量子信息的拓扑保护。

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.