163 lines
3.6 KiB
Plaintext
163 lines
3.6 KiB
Plaintext
---
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title: U1Gate
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description: API reference for qiskit.circuit.library.U1Gate
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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.U1Gate
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---
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# U1Gate
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<Class id="qiskit.circuit.library.U1Gate" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.20/qiskit/circuit/library/standard_gates/u1.py" signature="U1Gate(theta, label=None)" modifiers="class">
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Bases: `qiskit.circuit.gate.Gate`
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Single-qubit rotation about the Z axis.
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This is a diagonal gate. It can be implemented virtually in hardware via framechanges (i.e. at zero error and duration).
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**Circuit symbol:**
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```python
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┌───────┐
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q_0: ┤ U1(λ) ├
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└───────┘
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```
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**Matrix Representation:**
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$$
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\begin{split}U1(\lambda) =
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\begin{pmatrix}
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1 & 0 \\
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0 & e^{i\lambda}
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\end{pmatrix}\end{split}
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$$
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**Examples:**
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> $$
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> U1(\lambda = \pi) = Z
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> $$
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>
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> $$
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> U1(\lambda = \pi/2) = S
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> $$
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>
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> $$
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> U1(\lambda = \pi/4) = T
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> $$
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<Admonition title="See also" type="note">
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`RZGate`: This gate is equivalent to RZ up to a phase factor.
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> $$
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> U1(\lambda) = e^{i{\lambda}/2} RZ(\lambda)
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> $$
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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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Reference for virtual Z gate implementation: [1612.00858](https://arxiv.org/abs/1612.00858)
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</Admonition>
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Create new U1 gate.
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## Methods Defined Here
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### control
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<Function id="qiskit.circuit.library.U1Gate.control" signature="U1Gate.control(num_ctrl_qubits=1, label=None, ctrl_state=None)">
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Return a (multi-)controlled-U1 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.U1Gate.inverse" signature="U1Gate.inverse()">
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Return inverted U1 gate ($U1(\lambda){\dagger} = U1(-\lambda)$)
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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.U1Gate.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.U1Gate.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.U1Gate.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.U1Gate.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.U1Gate.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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### name
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<Attribute id="qiskit.circuit.library.U1Gate.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.U1Gate.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.U1Gate.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.U1Gate.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.U1Gate.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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