Graph States

Graph states are a type of quantum state that can be represented by a graph \(G\). The state defined by \(G\) is

\[|\psi\rangle = \prod_{i,j \in E(G)} CZ_{ij} |+\rangle^{\otimes n},\]

where \(n\) is the number of nodes, \(E(G)\) is the set of edges, and \(CZ_{ij}\) is the controlled-Z gate on qubits \(i\) and \(j\).


In mentpy we can create a graph state using the GraphState class:

In [1]: gr = mp.GraphState()

In [2]: gr.add_edges_from([(0, 1), (1, 2), (2, 0)])

In [3]: print(gr)
GraphState with 3 nodes and 3 edges


Graph states are a particular type of stabilizer state. We can get the stabilizer operators of such state using the stabilizers() method:

In [4]: stabs = gr.stabilizers()

In [5]: print(stabs)

To learn how to use graph states as resources for computation, see the Creating MBQC Circuits tutorial.