# 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 because 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.

Formally a cluster state is a state which obeys the set eigenvalue equations:

${\displaystyle K_{G}^{(a)}{\left|G\right\rangle }=(-1)^{k_{a}}{\left|G\right\rangle }}$

where

${\displaystyle K_{G}^{(a)}=\sigma _{x}^{(a)}\bigotimes _{b\in {\mathrm {N} }(a)}\sigma _{z}^{(b)}.}$

## References

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