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. 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. 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 where | + ⟩ = ( | 0 ⟩ + | 1 ⟩ ) / 2 {displaystyle {left|+ ight angle }=({left|0 ight angle }+{left|1 ight angle })/{sqrt {2}}} and the operator U { a , b } {displaystyle U^{{a,b}}} is the controlled-Z interaction between the two vertices (qubits) a, b