136 lines
3.2 KiB
Plaintext
136 lines
3.2 KiB
Plaintext
---
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title: UGate
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description: API reference for qiskit.circuit.library.UGate
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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.UGate
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---
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# UGate
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<Class id="qiskit.circuit.library.UGate" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.19/qiskit/circuit/library/standard_gates/u.py" signature="UGate(theta, phi, lam, label=None)" modifiers="class">
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Bases: `qiskit.circuit.gate.Gate`
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Generic single-qubit rotation gate with 3 Euler angles.
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Implemented using two X90 pulses on IBM Quantum systems:
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$$
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U(\theta, \phi, \lambda) =
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RZ(\phi - \pi/2) RX(\pi/2) RZ(\pi - \theta) RX(\pi/2) RZ(\lambda - \pi/2)
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$$
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**Circuit symbol:**
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```python
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┌──────────┐
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q_0: ┤ U(ϴ,φ,λ) ├
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└──────────┘
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```
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**Matrix Representation:**
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$$
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\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}U(\theta, \phi, \lambda) =
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\begin{pmatrix}
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\cos(\th) & -e^{i\lambda}\sin(\th) \\
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e^{i\phi}\sin(\th) & e^{i(\phi+\lambda)}\cos(\th)
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\end{pmatrix}\end{split}\end{aligned}\end{align}
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$$
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**Examples:**
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$$
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U\left(\theta, -\frac{\pi}{2}, \frac{\pi}{2}\right) = RX(\theta)
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$$
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$$
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U(\theta, 0, 0) = RY(\theta)
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$$
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Create new U gate.
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## Methods Defined Here
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### control
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<Function id="qiskit.circuit.library.UGate.control" signature="UGate.control(num_ctrl_qubits=1, label=None, ctrl_state=None)">
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Return a (multi-)controlled-U gate.
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**Parameters**
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* **num\_ctrl\_qubits** (*int*) – number of control qubits.
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* **label** (*str or None*) – An optional label for the gate \[Default: None]
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* **ctrl\_state** (*int or str or None*) – control state expressed as integer, string (e.g. ‘110’), or None. If None, use all 1s.
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**Returns**
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controlled version of this gate.
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**Return type**
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[ControlledGate](qiskit.circuit.ControlledGate "qiskit.circuit.ControlledGate")
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</Function>
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### inverse
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<Function id="qiskit.circuit.library.UGate.inverse" signature="UGate.inverse()">
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Return inverted U gate.
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$U(\theta,\phi,\lambda)^{\dagger} =U(-\theta,-\lambda,-\phi)$)
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</Function>
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## Attributes
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### condition\_bits
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<Attribute id="qiskit.circuit.library.UGate.condition_bits">
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Get Clbits in condition.
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**Return type**
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`List`\[`Clbit`]
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</Attribute>
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### decompositions
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<Attribute id="qiskit.circuit.library.UGate.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.UGate.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.UGate.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.UGate.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.UGate.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.UGate.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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