107 lines
2.3 KiB
Plaintext
107 lines
2.3 KiB
Plaintext
---
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title: U2Gate
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description: API reference for qiskit.circuit.library.U2Gate
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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.U2Gate
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---
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# U2Gate
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<Class id="qiskit.circuit.library.U2Gate" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.18/qiskit/circuit/library/standard_gates/u2.py" signature="U2Gate(phi, lam, label=None)" modifiers="class">
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Bases: `qiskit.circuit.gate.Gate`
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Single-qubit rotation about the X+Z axis.
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Implemented using one X90 pulse on IBM Quantum systems:
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$$
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U2(\phi, \lambda) = RZ(\phi).RY(\frac{\pi}{2}).RZ(\lambda)
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$$
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**Circuit symbol:**
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```python
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┌─────────┐
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q_0: ┤ U2(φ,λ) ├
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└─────────┘
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```
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**Matrix Representation:**
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$$
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\begin{split}U2(\phi, \lambda) = \frac{1}{\sqrt{2}}
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\begin{pmatrix}
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1 & -e^{i\lambda} \\
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e^{i\phi} & e^{i(\phi+\lambda)}
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\end{pmatrix}\end{split}
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$$
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**Examples:**
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$$
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U2(0, \pi) = H
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U2(0, 0) = RY(\pi/2)
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U2(-\pi/2, \pi/2) = RX(\pi/2)
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$$
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<Admonition title="See also" type="note">
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`U3Gate`: U3 is a generalization of U2 that covers all single-qubit rotations, using two X90 pulses.
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</Admonition>
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Create new U2 gate.
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## Methods Defined Here
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### inverse
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<Function id="qiskit.circuit.library.U2Gate.inverse" signature="U2Gate.inverse()">
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Return inverted U2 gate.
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$U2(\phi, \lambda)^{\dagger} =U2(-\lambda-\pi, -\phi+\pi)$)
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</Function>
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## Attributes
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### decompositions
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<Attribute id="qiskit.circuit.library.U2Gate.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.U2Gate.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.U2Gate.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.U2Gate.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.U2Gate.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.U2Gate.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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