Cluster state

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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:

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


K_{G}^{(a)} = \sigma_x^{(a)} \bigotimes_{b\in \mathrm{N}(a)} \sigma_z^{(b)}.

with N(a) denoting the neighbourhood of a.

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