g`~dZddlmZddlZddlmZmZddlm Z ddl m Z GddeZ Gd d eZ dS) zGraph State circuit and gate.) annotationsN)QuantumCircuitGate) CircuitError)deprecate_funccLeZdZdZedddd fd ZxZS) GraphStateaCircuit 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)) _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 `_ z1.3z2Use qiskit.circuit.library.GraphStateGate instead.T)sinceadditional_msgpendingadjacency_matrixlist | np.ndarrayreturnNonecJtj|}tj||st dt |}t |jd|| ||j ddS)a+Create 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)selfr graph_state_gate __class__s X/granary/edev/quantum/lib/python3.11/site-packages/qiskit/circuit/library/graph_state.pyrzGraphState.__init__=s$:&677{+-=-G-G-I-IJJ JHII I)*:;; )4;WEU;W;WXXX %dk4 HHHHHr rrr)__name__ __module__ __qualname____doc__rr __classcell__r"s@r#r r s{##J^K IIIII  IIIIIr$r cLeZdZdZd fd ZdZdZed Zd Z xZ S) raA 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 `_ r rrrctj|}tj||st dt |}t d||gdS)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)r r rr"s r#rzGraphStateGate.__init__s:&677{+-=-G-G-I-IJJ JHII I)**  m L\K]^^^^^r$cZ|j}t|j|j}|t |jt |jD]E}t |dz|jD]*}|||dkr|||+F||_dS)Nr)r rrrhrangecz definition)r r circuitijs r#_definezGraphStateGate._defines0 tyAAA %(()))t'' % %A1q5$/22 % %#A&q)Q..JJq!$$$ %"r$c|S)zParameter validation)r parameters r#validate_parameterz!GraphStateGate.validate_parametersr$c|jdS)zReturns the adjacency matrix.r)r/)r s r#r zGraphStateGate.adjacency_matrixs{1~r$ct|to1|j|jko!tj|j|jkS)N) isinstancerrrallr )r others r#__eq__zGraphStateGate.__eq__sE un - - H5#33 Ht,0FFGG r$r%) r&r'r(r)rr:r>propertyr rDr*r+s@r#rrXs&&P______$"""X       r$r)r) __future__rnumpyrqiskit.circuit.quantumcircuitrrqiskit.circuit.exceptionsrqiskit.utils.deprecationrr rr<r$r#rKs$#"""""">>>>>>>>222222333333>I>I>I>I>I>I>I>IBS S S S S TS S S S S r$