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# GraphState¶

ベースクラス: QuantumCircuit

Circuit 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

$|G\rangle = \prod_{(a,b) \in E} CZ_{(a,b)} {|+\rangle}^{\otimes V}$

Such a state can be prepared by first preparing all qubits in the $$+$$ state, then applying a $$CZ$$ 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:

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

Create graph state preparation circuit.

パラメータ

adjacency_matrix (list | np.ndarray) – input graph as n-by-n list of 0-1 lists

CircuitError – If adjacency_matrix is not symmetric.

The circuit prepares a graph state with the given adjacency matrix.

Attributes

ancillas

Returns a list of ancilla bits in the order that the registers were added.

calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form {'gate_name': {(qubits, params): schedule}}

clbits

Returns a list of classical bits in the order that the registers were added.

data

Return the circuit data (instructions and context).

a list-like object containing the CircuitInstructions for each instruction.

QuantumCircuitData

extension_lib = 'include "qelib1.inc";'
global_phase

Return the global phase of the circuit in radians.

header = 'OPENQASM 2.0;'
instances = 151
layout

Return any associated layout information anout the circuit

This attribute contains an optional TranspileLayout object. This is typically set on the output from transpile() or PassManager.run() to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the transpile() function, an initial layout which permutes the qubits based on the selected physical qubits on the Target, and a final layout which is an output permutation caused by SwapGates inserted during routing.

The user provided metadata associated with the circuit.

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

num_ancillas

Return the number of ancilla qubits.

num_clbits

Return number of classical bits.

num_parameters

The number of parameter objects in the circuit.

num_qubits

Return number of qubits.

op_start_times

Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.

AttributeError – When circuit is not scheduled.

parameters

The parameters defined in the circuit.

This attribute returns the Parameter objects in the circuit sorted alphabetically. Note that parameters instantiated with a ParameterVector are still sorted numerically.

サンプル

The snippet below shows that insertion order of parameters does not matter.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters  # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])


Bear in mind that alphabetical sorting might be unituitive when it comes to numbers. The literal 「10」 comes before 「2」 in strict alphabetical sorting.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
┌─────────────────────────────┐
q: ┤ U(angle_1,angle_2,angle_10) ├
└─────────────────────────────┘
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])


To respect numerical sorting, a ParameterVector can be used.



>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
...     circuit.rx(x_i, 0)
>>> circuit.parameters
ParameterView([
ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
..., ParameterVectorElement(x[11])
])


The sorted Parameter objects in the circuit.

prefix = 'circuit'
qubits

Returns a list of quantum bits in the order that the registers were added.