z ipSrSSKJr SSKrSSKJrJr SSKJ r SSK J r "SS\5r "S S \5r g) zGraph State circuit and gate.) annotationsN)QuantumCircuitGate) CircuitError)deprecate_funccF^\rSrSrSr\"SSSS9S U4Sjj5rSrU=r$) GraphStateaVCircuit to prepare a graph state. Given a graph G = (V, E), with the set of vertices V and the set of edges E, the corresponding graph state is defined as .. math:: |G\rangle = \prod_{(a,b) \in E} CZ_{(a,b)} {|+\rangle}^{\otimes V} Such a state can be prepared by first preparing all qubits in the :math:`+` state, then applying a :math:`CZ` gate for each corresponding graph edge. Graph state preparation circuits are Clifford circuits, and thus easy to simulate classically. However, by adding a layer of measurements in a product basis at the end, there is evidence that the circuit becomes hard to simulate [2]. Reference Circuit: .. plot:: :alt: Diagram illustrating the previously described circuit. from qiskit.circuit.library import GraphState from qiskit.visualization.library import _generate_circuit_library_visualization import rustworkx as rx G = rx.generators.cycle_graph(5) circuit = GraphState(rx.adjacency_matrix(G)) circuit.name = "Graph state" _generate_circuit_library_visualization(circuit) References: [1] M. Hein, J. Eisert, H.J. Briegel, Multi-party Entanglement in Graph States, `arXiv:0307130 `_ [2] D. Koh, Further Extensions of Clifford Circuits & their Classical Simulation Complexities. `arXiv:1512.07892 `_ z2.1z2Use qiskit.circuit.library.GraphStateGate instead.z in Qiskit 3.0)sinceadditional_msgremoval_timelinec>[R"U5n[R"XR55(d [ S5e[ U5n[ TU]URSU3S9 URX RSS9 g)zCreate graph state preparation circuit. Args: adjacency_matrix: input graph as n-by-n list of 0-1 lists Raises: CircuitError: If adjacency_matrix is not symmetric. The circuit prepares a graph state with the given adjacency matrix. 'The adjacency matrix must be symmetric.zgraph: nameT)qubitsinplaceN) npasarrayallclose transposerGraphStateGatesuper__init__ num_qubitscomposer)selfadjacency_matrixgraph_state_gate __class__s \/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/graph_state.pyrGraphState.__init__>s}$::&67{{+-G-G-IJJHI I)*:; )44WEUDV;WX %kk4 Hrzlist | np.ndarrayreturnNone) __name__ __module__ __qualname____firstlineno____doc__rr__static_attributes__ __classcell__r s@r!r r s-$LK( I  Ir#r cR^\rSrSrSrS U4SjjrSrSr\S5r Sr Sr U=r $) rYaJA gate representing a graph state. Given a graph G = (V, E), with the set of vertices V and the set of edges E, the corresponding graph state is defined as .. math:: |G\rangle = \prod_{(a,b) \in E} CZ_{(a,b)} {|+\rangle}^{\otimes V} Such a state can be prepared by first preparing all qubits in the :math:`+` state, then applying a :math:`CZ` gate for each corresponding graph edge. Graph state preparation circuits are Clifford circuits, and thus easy to simulate classically. However, by adding a layer of measurements in a product basis at the end, there is evidence that the circuit becomes hard to simulate [2]. Reference Circuit: .. plot:: :alt: Circuit diagram output by the previous code. :include-source: from qiskit.circuit import QuantumCircuit from qiskit.circuit.library import GraphStateGate import rustworkx as rx G = rx.generators.cycle_graph(5) circuit = QuantumCircuit(5) circuit.append(GraphStateGate(rx.adjacency_matrix(G)), [0, 1, 2, 3, 4]) circuit.decompose().draw('mpl') References: [1] M. Hein, J. Eisert, H.J. Briegel, Multi-party Entanglement in Graph States, `arXiv:0307130 `_ [2] D. Koh, Further Extensions of Clifford Circuits & their Classical Simulation Complexities. `arXiv:1512.07892 `_ c>[R"U5n[R"XR55(d [ S5e[ U5n[ TU]SX!/S9 g)z Args: adjacency_matrix: input graph as n-by-n list of 0-1 lists Raises: CircuitError: If adjacency_matrix is not symmetric. The gate represents a graph state with the given adjacency matrix. r graph_state)rrparamsN)rrrrrlenrr)rrrr s r!rGraphStateGate.__init__sZ::&67{{+-G-G-IJJHI I)*  m K]^r#c`URn[URURS9nUR [ UR55 [ UR5HAn[ US-UR5H!nXUS:XdMUR X45 M# MC X lg)Nr)rrrrhrangecz definition)rrcircuitijs r!_defineGraphStateGate._defines00 tyyA %()t'A1q5$//2#&q)Q.JJq$3("r#cU$)zParameter validationr$)r parameters r!validate_parameter!GraphStateGate.validate_parametersr#c URS$)zReturns the adjacency matrix.r)r4)rs r!rGraphStateGate.adjacency_matrixs{{1~r#c[U[5=(aM URUR:H=(a- [R"UR UR :H5$)N) isinstancerrrallr)rothers r!__eq__GraphStateGate.__eq__sL un - H5#3#33 Ht,,0F0FFG r#)r<r%) r(r)r*r+r,rr@rDpropertyrrLr-r.r/s@r!rrYs7'R_$"  r#r)r, __future__rnumpyrqiskit.circuit.quantumcircuitrrqiskit.circuit.exceptionsrqiskit.utils.deprecationrr rr$r#r!rTs6$">23?I?IDT TT r#