Quantum Double Cluster States

Courtney Brell
Event Date and Time: 
Tue, 2012-08-28 09:30 - 11:00
Hennings 318
Local Contact: 
Robert Raussendorf
Intended Audience: 
The toric code and the cluster state are related in a few ways. Perhaps most straightforwardly, the toric code state can be prepared by single qubit measurements on a cluster state. The cluster state can also be used to implement topologically protected computation by simulating the braiding of topological defects in the toric code. The toric code is the simplest member of a family of models called the Kitaev quantum double models. This is a class of lattice spin models whose excitations are described by anyons. Significantly, in some cases these anyons can be non-abelian and can implement universal quantum computation by braiding. We make use of the relationship between the toric code and cluster state to define generalized cluster states corresponding to each quantum double model, and show that analogous relationships hold between these Quantum Double Cluster States (QDCS) and the Kitaev quantum double models. We explore the use of QDCS for topological cluster state computation, and find that it may be most suited to implementation in an adiabatic architecture, as opposed to the measurement-based scheme that is typically envisaged. In doing so, we describe a protocol for universal topologically protected adiabatic quantum computation.
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