201 lines
5.3 KiB
Plaintext
201 lines
5.3 KiB
Plaintext
---
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title: GraphState
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description: API reference for qiskit.circuit.library.GraphState
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.circuit.library.GraphState
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---
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# GraphState
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<Class id="qiskit.circuit.library.GraphState" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.20/qiskit/circuit/library/graph_state.py" signature="GraphState(adjacency_matrix)" modifiers="class">
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Bases: `qiskit.circuit.quantumcircuit.QuantumCircuit`
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Circuit to prepare a graph state.
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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
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$$
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|G\rangle = \prod_{(a,b) \in E} CZ_{(a,b)} {|+\rangle}^{\otimes V}
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$$
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Such a state can be prepared by first preparing all qubits in the $+$ state, then applying a $CZ$ gate for each corresponding graph edge.
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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].
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**Reference Circuit:**
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**References:**
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**\[1] M. Hein, J. Eisert, H.J. Briegel, Multi-party Entanglement in Graph States,**
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[arXiv:0307130](https://arxiv.org/pdf/quant-ph/0307130.pdf)
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**\[2] D. Koh, Further Extensions of Clifford Circuits & their Classical Simulation Complexities.**
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[arXiv:1512.07892](https://arxiv.org/pdf/1512.07892.pdf)
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Create graph state preparation circuit.
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**Parameters**
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**adjacency\_matrix** (`Union`\[`List`, `array`]) – input graph as n-by-n list of 0-1 lists
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**Raises**
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**CircuitError** – If adjacency\_matrix is not symmetric.
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The circuit prepares a graph state with the given adjacency matrix.
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## Attributes
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### ancillas
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<Attribute id="qiskit.circuit.library.GraphState.ancillas">
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Returns a list of ancilla bits in the order that the registers were added.
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**Return type**
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`List`\[`AncillaQubit`]
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</Attribute>
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### calibrations
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<Attribute id="qiskit.circuit.library.GraphState.calibrations">
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Return calibration dictionary.
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**The custom pulse definition of a given gate is of the form**
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\{‘gate\_name’: \{(qubits, params): schedule}}
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**Return type**
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`dict`
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</Attribute>
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### clbits
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<Attribute id="qiskit.circuit.library.GraphState.clbits">
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Returns a list of classical bits in the order that the registers were added.
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**Return type**
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`List`\[`Clbit`]
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</Attribute>
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### data
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<Attribute id="qiskit.circuit.library.GraphState.data">
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Return the circuit data (instructions and context).
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**Returns**
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a list-like object containing the tuples for the circuit’s data.
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Each tuple is in the format `(instruction, qargs, cargs)`, where instruction is an Instruction (or subclass) object, qargs is a list of Qubit objects, and cargs is a list of Clbit objects.
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**Return type**
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QuantumCircuitData
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</Attribute>
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### extension\_lib
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<Attribute id="qiskit.circuit.library.GraphState.extension_lib" attributeValue="'include "qelib1.inc";'" />
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### global\_phase
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<Attribute id="qiskit.circuit.library.GraphState.global_phase">
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Return the global phase of the circuit in radians.
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**Return type**
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`Union`\[`ParameterExpression`, `float`]
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</Attribute>
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### header
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<Attribute id="qiskit.circuit.library.GraphState.header" attributeValue="'OPENQASM 2.0;'" />
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### instances
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<Attribute id="qiskit.circuit.library.GraphState.instances" attributeValue="9" />
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### metadata
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<Attribute id="qiskit.circuit.library.GraphState.metadata">
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The user provided metadata associated with the circuit
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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.
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**Return type**
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`dict`
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</Attribute>
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### num\_ancillas
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<Attribute id="qiskit.circuit.library.GraphState.num_ancillas">
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Return the number of ancilla qubits.
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**Return type**
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`int`
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</Attribute>
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### num\_clbits
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<Attribute id="qiskit.circuit.library.GraphState.num_clbits">
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Return number of classical bits.
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**Return type**
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`int`
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</Attribute>
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### num\_parameters
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<Attribute id="qiskit.circuit.library.GraphState.num_parameters">
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Convenience function to get the number of parameter objects in the circuit.
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**Return type**
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`int`
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.circuit.library.GraphState.num_qubits">
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Return number of qubits.
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**Return type**
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`int`
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</Attribute>
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### parameters
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<Attribute id="qiskit.circuit.library.GraphState.parameters">
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Convenience function to get the parameters defined in the parameter table.
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**Return type**
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`ParameterView`
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</Attribute>
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### prefix
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<Attribute id="qiskit.circuit.library.GraphState.prefix" attributeValue="'circuit'" />
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### qubits
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<Attribute id="qiskit.circuit.library.GraphState.qubits">
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Returns a list of quantum bits in the order that the registers were added.
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**Return type**
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`List`\[`Qubit`]
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</Attribute>
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</Class>
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