149 lines
3.2 KiB
Plaintext
149 lines
3.2 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/0.25/qiskit/circuit/library/standard_gates/u2.py" signature="qiskit.circuit.library.U2Gate(phi, lam, label=None)" modifiers="class">
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Bases: [`Gate`](qiskit.circuit.Gate "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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<Admonition title="Warning" type="caution">
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This gate is deprecated. Instead, the following replacements should be used
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$$
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U2(\phi, \lambda) = U\left(\frac{\pi}{2}, \phi, \lambda\right)
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$$
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```python
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circuit = QuantumCircuit(1)
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circuit.u(pi/2, phi, lambda)
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```
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</Admonition>
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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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$$
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U2(\phi,\lambda) = e^{i \frac{\phi + \lambda}{2}}RZ(\phi)
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RY\left(\frac{\pi}{2}\right) RZ(\lambda)
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= e^{- i\frac{\pi}{4}} P\left(\frac{\pi}{2} + \phi\right)
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\sqrt{X} P\left(\lambda- \frac{\pi}{2}\right)
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$$
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$$
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U2(0, \pi) = H
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$$
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$$
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U2(0, 0) = RY(\pi/2)
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$$
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$$
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U2(-\pi/2, \pi/2) = RX(\pi/2)
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$$
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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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## Attributes
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### condition\_bits
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<Attribute id="qiskit.circuit.library.U2Gate.condition_bits">
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Get Clbits in condition.
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</Attribute>
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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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</Attribute>
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### name
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<Attribute id="qiskit.circuit.library.U2Gate.name">
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Return the name.
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</Attribute>
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### num\_clbits
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<Attribute id="qiskit.circuit.library.U2Gate.num_clbits">
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Return the number of clbits.
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.circuit.library.U2Gate.num_qubits">
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Return the number of qubits.
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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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## Methods
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### inverse
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<Function id="qiskit.circuit.library.U2Gate.inverse" signature="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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</Class>
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