Cluster state

In quantum information and quantum computing, a cluster state is a type of highly entangled state of multiple qubits. Cluster states are generated in lattices of qubits with Ising type interactions. A cluster C is a connected subset of a d-dimensional lattice, and a cluster state is a pure state of the qubits located on C. They are different from other types of entangled states such as GHZ states or W states in that it is more difficult to eliminate quantum entanglement (via projective measurements) in the case of cluster states. Another way of thinking of cluster states is as a particular instance of graph states, where the underlying graph is a connected subset of a d-dimensional lattice. Cluster states are especially useful in the context of the one-way quantum computer. For a comprehensible introduction to the topic see.

Formally, cluster states | ϕ { κ } ⟩ C are states which obey the set eigenvalue equations:

where K ( a ) are the correlation operators

with σ x and σ z being Pauli matrices, N ( a ) denoting the neighbourhood of a and { κ a ∈ { 0 , 1 } | a ∈ C } being a set of binary parameters specifying the particular instance of a cluster state.

Cluster states have been realized experimentally. They have been obtained in photonic experiments using parametric downconversion . They have been created also in optical lattices of cold atoms .