172 lines
4.9 KiB
Plaintext
172 lines
4.9 KiB
Plaintext
---
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title: CU1Gate
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description: API reference for qiskit.circuit.library.CU1Gate
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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.CU1Gate
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---
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# CU1Gate
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<Class id="qiskit.circuit.library.CU1Gate" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.25/qiskit/circuit/library/standard_gates/u1.py" signature="qiskit.circuit.library.CU1Gate(theta, label=None, ctrl_state=None)" modifiers="class">
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Bases: [`ControlledGate`](qiskit.circuit.ControlledGate "qiskit.circuit.controlledgate.ControlledGate")
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Controlled-U1 gate.
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This is a diagonal and symmetric gate that induces a phase on the state of the target qubit, depending on the control state.
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**Circuit symbol:**
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```python
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q_0: ─■──
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│λ
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q_1: ─■──
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```
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**Matrix representation:**
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$$
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\begin{split}CU1(\lambda) =
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I \otimes |0\rangle\langle 0| + U1 \otimes |1\rangle\langle 1| =
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\begin{pmatrix}
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1 & 0 & 0 & 0 \\
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0 & 1 & 0 & 0 \\
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0 & 0 & 1 & 0 \\
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0 & 0 & 0 & e^{i\lambda}
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\end{pmatrix}\end{split}
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$$
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<Admonition title="See also" type="note">
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`CRZGate`: Due to the global phase difference in the matrix definitions of U1 and RZ, CU1 and CRZ are different gates with a relative phase difference.
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</Admonition>
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Create new CU1 gate.
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## Attributes
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### condition\_bits
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<Attribute id="qiskit.circuit.library.CU1Gate.condition_bits">
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Get Clbits in condition.
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</Attribute>
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### ctrl\_state
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<Attribute id="qiskit.circuit.library.CU1Gate.ctrl_state">
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Return the control state of the gate as a decimal integer.
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</Attribute>
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### decompositions
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<Attribute id="qiskit.circuit.library.CU1Gate.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.CU1Gate.definition">
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Return definition in terms of other basic gates. If the gate has open controls, as determined from self.ctrl\_state, the returned definition is conjugated with X without changing the internal \_definition.
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</Attribute>
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### duration
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<Attribute id="qiskit.circuit.library.CU1Gate.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.CU1Gate.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.CU1Gate.name">
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Get name of gate. If the gate has open controls the gate name will become:
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> \<original\_name\_o\<ctrl\_state>
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where \<original\_name> is the gate name for the default case of closed control qubits and \<ctrl\_state> is the integer value of the control state for the gate.
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</Attribute>
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### num\_clbits
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<Attribute id="qiskit.circuit.library.CU1Gate.num_clbits">
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Return the number of clbits.
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</Attribute>
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### num\_ctrl\_qubits
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<Attribute id="qiskit.circuit.library.CU1Gate.num_ctrl_qubits">
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Get number of control qubits.
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**Returns**
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The number of control qubits for the gate.
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**Return type**
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[int](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)")
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.circuit.library.CU1Gate.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.CU1Gate.params">
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Get parameters from base\_gate.
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**Returns**
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List of gate parameters.
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**Return type**
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[list](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.12)")
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**Raises**
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[**CircuitError**](circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – Controlled gate does not define a base gate
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</Attribute>
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### unit
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<Attribute id="qiskit.circuit.library.CU1Gate.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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### control
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<Function id="qiskit.circuit.library.CU1Gate.control" signature="control(num_ctrl_qubits=1, label=None, ctrl_state=None)">
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Controlled version of this gate.
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**Parameters**
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* **num\_ctrl\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)")) – number of control qubits.
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* **label** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.12)") *or None*) – An optional label for the gate \[Default: None]
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* **ctrl\_state** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)") *or*[*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.12)") *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.CU1Gate.inverse" signature="inverse()">
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Return inverted CU1 gate ($CU1(\lambda)^{\dagger} = CU1(-\lambda)$)
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</Function>
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</Class>
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