What is "cluster state"

n. (context physics English) Any of a subset of graph states that can be fitted to a regular cubic lattice

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⟩ are states which obey the set eigenvalue equations:

where K are the correlation operators

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

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