Graph state

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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[edit]

Given a graph G = (VE), with the set of vertices V and the set of edges E, the corresponding graph state is defined as

where the operator is the controlled-Z interaction between the two vertices (qubits) a, b


Alternative definition[edit]

An alternative and equivalent definition is the following.

Define an operator for each vertex a of G:

where N(a) is the neighborhood of a (that is, the set of all b such that ) and are the pauli matrices. The graph state is then defined as the simultaneous eigenstate of the operators with eigenvalue 1:

See also[edit]