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:

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

where

$K_{G}^{(a)} = \sigma_x^{(a)} \otimes_{b\in nghb(a)} \sigma_z^{(b)}.$

See also

• Bell state
• Graph state

References

• H. J. Briegel and R. Raussendorf (2001). "Persistent Entanglement in arrays of Interacting Particles". Physical Review Letters 86 (5): 910–3. Bibcode 2001PhRvL..86..910B. doi:10.1103/PhysRevLett.86.910. PMID 11177971.