115 lines
3.3 KiB
Plaintext
115 lines
3.3 KiB
Plaintext
---
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title: ECRGate
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description: API reference for qiskit.circuit.library.ECRGate
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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.ECRGate
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---
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# ECRGate
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<Class id="qiskit.circuit.library.ECRGate" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.18/qiskit/circuit/library/standard_gates/ecr.py" signature="ECRGate" modifiers="class">
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Bases: `qiskit.circuit.gate.Gate`
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An echoed RZX(pi/2) gate implemented using RZX(pi/4) and RZX(-pi/4).
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This gate is maximally entangling and is equivalent to a CNOT up to single-qubit pre-rotations. The echoing procedure mitigates some unwanted terms (terms other than ZX) to cancel in an experiment.
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**Circuit Symbol:**
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```python
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┌─────────┐ ┌────────────┐┌────────┐┌─────────────┐
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q_0: ┤0 ├ q_0: ┤0 ├┤ RX(pi) ├┤0 ├
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│ ECR │ = │ RZX(pi/4) │└────────┘│ RZX(-pi/4) │
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q_1: ┤1 ├ q_1: ┤1 ├──────────┤1 ├
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└─────────┘ └────────────┘ └─────────────┘
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```
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**Matrix Representation:**
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$$
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\begin{split}ECR\ q_0, q_1 = \frac{1}{\sqrt{2}}
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\begin{pmatrix}
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0 & 1 & 0 & i \\
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1 & 0 & -i & 0 \\
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0 & i & 0 & 1 \\
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-i & 0 & 1 & 0
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\end{pmatrix}\end{split}
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$$
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<Admonition title="Note" type="note">
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In Qiskit’s convention, higher qubit indices are more significant (little endian convention). In the above example we apply the gate on (q\_0, q\_1) which results in the $X \otimes Z$ tensor order. Instead, if we apply it on (q\_1, q\_0), the matrix will be $Z \otimes X$:
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```python
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┌─────────┐
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q_0: ┤1 ├
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│ ECR │
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q_1: ┤0 ├
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└─────────┘
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```
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$$
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\begin{split}ECR\ q_0, q_1 = \frac{1}{\sqrt{2}}
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\begin{pmatrix}
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0 & 0 & 1 & i \\
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0 & 0 & i & 1 \\
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1 & -i & 0 & 0 \\
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-i & 1 & 0 & 0
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\end{pmatrix}\end{split}
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$$
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</Admonition>
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Create new ECR gate.
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## Methods Defined Here
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### to\_matrix
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<Function id="qiskit.circuit.library.ECRGate.to_matrix" signature="ECRGate.to_matrix()">
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Return a numpy.array for the ECR gate.
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</Function>
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## Attributes
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### decompositions
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<Attribute id="qiskit.circuit.library.ECRGate.decompositions">
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Get the decompositions of the instruction from the SessionEquivalenceLibrary.
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</Attribute>
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### definition
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<Attribute id="qiskit.circuit.library.ECRGate.definition">
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Return definition in terms of other basic gates.
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</Attribute>
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### duration
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<Attribute id="qiskit.circuit.library.ECRGate.duration">
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Get the duration.
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</Attribute>
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### label
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<Attribute id="qiskit.circuit.library.ECRGate.label">
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Return instruction label
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**Return type**
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`str`
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</Attribute>
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### params
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<Attribute id="qiskit.circuit.library.ECRGate.params">
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return instruction params.
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</Attribute>
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### unit
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<Attribute id="qiskit.circuit.library.ECRGate.unit">
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Get the time unit of duration.
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</Attribute>
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</Class>
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