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graph state : ウィキペディア英語版
graph state

In quantum computing, a graph state is a special type of multi-qubit state that can be represented by a graph. Each qubit is represented by a vertex of the graph, and there is an edge between every interacting pair of qubits. In particular, they are a convenient way of representing certain types of entangled states.
Graph states are useful in quantum error-correcting codes, entanglement measurement and purification and for characterization of computational resources in measurement based quantum computing models.
== Formal definition ==

Given a graph ''G'' = (''V'', ''E''), with the set of vertices ''V'' and the set of edges ''E'', the corresponding graph state is defined as
: =\prod _U^ ^
where the operator U^ is the controlled-''Z'' interaction between the two vertices (qubits) ''a'', ''b''
: U^ =\left( & & & \\ & & & \\ & & & \\ & & & \end\right )
And
: =\frac + }

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