368 lines
14 KiB
Plaintext
368 lines
14 KiB
Plaintext
---
|
||
title: U1Gate
|
||
description: API reference for qiskit.circuit.library.U1Gate
|
||
in_page_toc_min_heading_level: 1
|
||
python_api_type: class
|
||
python_api_name: qiskit.circuit.library.U1Gate
|
||
---
|
||
|
||
<span id="qiskit-circuit-library-u1gate" />
|
||
|
||
# qiskit.circuit.library.U1Gate
|
||
|
||
<Class id="qiskit.circuit.library.U1Gate" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.16/qiskit/circuit/library/standard_gates/u1.py" signature="U1Gate(theta, label=None)" modifiers="class">
|
||
Single-qubit rotation about the Z axis.
|
||
|
||
This is a diagonal gate. It can be implemented virtually in hardware via framechanges (i.e. at zero error and duration).
|
||
|
||
**Circuit symbol:**
|
||
|
||
```python
|
||
┌───────┐
|
||
q_0: ┤ U1(λ) ├
|
||
└───────┘
|
||
```
|
||
|
||
**Matrix Representation:**
|
||
|
||
$$
|
||
\begin{split}U1(\lambda) =
|
||
\begin{pmatrix}
|
||
1 & 0 \\
|
||
0 & e^{i\lambda}
|
||
\end{pmatrix}\end{split}
|
||
$$
|
||
|
||
**Examples:**
|
||
|
||
> $$
|
||
> U1(\lambda = \pi) = Z
|
||
> $$
|
||
>
|
||
> $$
|
||
> U1(\lambda = \pi/2) = S
|
||
> $$
|
||
>
|
||
> $$
|
||
> U1(\lambda = \pi/4) = T
|
||
> $$
|
||
|
||
<Admonition title="See also" type="note">
|
||
`RZGate`: This gate is equivalent to RZ up to a phase factor.
|
||
|
||
> $$
|
||
> U1(\lambda) = e^{i{\lambda}/2} RZ(\lambda)
|
||
> $$
|
||
|
||
`U3Gate`: U3 is a generalization of U2 that covers all single-qubit rotations, using two X90 pulses.
|
||
|
||
Reference for virtual Z gate implementation: [1612.00858](https://arxiv.org/abs/1612.00858)
|
||
</Admonition>
|
||
|
||
Create new U1 gate.
|
||
|
||
### \_\_init\_\_
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.__init__" signature="__init__(theta, label=None)">
|
||
Create new U1 gate.
|
||
</Function>
|
||
|
||
## Methods
|
||
|
||
| | |
|
||
| --------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------ |
|
||
| [`__init__`](#qiskit.circuit.library.U1Gate.__init__ "qiskit.circuit.library.U1Gate.__init__")(theta\[, label]) | Create new U1 gate. |
|
||
| [`add_decomposition`](#qiskit.circuit.library.U1Gate.add_decomposition "qiskit.circuit.library.U1Gate.add_decomposition")(decomposition) | Add a decomposition of the instruction to the SessionEquivalenceLibrary. |
|
||
| [`assemble`](#qiskit.circuit.library.U1Gate.assemble "qiskit.circuit.library.U1Gate.assemble")() | Assemble a QasmQobjInstruction |
|
||
| [`broadcast_arguments`](#qiskit.circuit.library.U1Gate.broadcast_arguments "qiskit.circuit.library.U1Gate.broadcast_arguments")(qargs, cargs) | Validation and handling of the arguments and its relationship. |
|
||
| [`c_if`](#qiskit.circuit.library.U1Gate.c_if "qiskit.circuit.library.U1Gate.c_if")(classical, val) | Add classical condition on register classical and value val. |
|
||
| [`control`](#qiskit.circuit.library.U1Gate.control "qiskit.circuit.library.U1Gate.control")(\[num\_ctrl\_qubits, label, ctrl\_state]) | Return a (mutli-)controlled-U1 gate. |
|
||
| [`copy`](#qiskit.circuit.library.U1Gate.copy "qiskit.circuit.library.U1Gate.copy")(\[name]) | Copy of the instruction. |
|
||
| [`inverse`](#qiskit.circuit.library.U1Gate.inverse "qiskit.circuit.library.U1Gate.inverse")() | Return inverted U1 gate ($U1(\lambda){\dagger} = U1(-\lambda)$) |
|
||
| [`is_parameterized`](#qiskit.circuit.library.U1Gate.is_parameterized "qiskit.circuit.library.U1Gate.is_parameterized")() | Return True .IFF. |
|
||
| [`mirror`](#qiskit.circuit.library.U1Gate.mirror "qiskit.circuit.library.U1Gate.mirror")() | DEPRECATED: use instruction.reverse\_ops(). |
|
||
| [`power`](#qiskit.circuit.library.U1Gate.power "qiskit.circuit.library.U1Gate.power")(exponent) | Creates a unitary gate as gate^exponent. |
|
||
| [`qasm`](#qiskit.circuit.library.U1Gate.qasm "qiskit.circuit.library.U1Gate.qasm")() | Return a default OpenQASM string for the instruction. |
|
||
| [`repeat`](#qiskit.circuit.library.U1Gate.repeat "qiskit.circuit.library.U1Gate.repeat")(n) | Creates an instruction with gate repeated n amount of times. |
|
||
| [`reverse_ops`](#qiskit.circuit.library.U1Gate.reverse_ops "qiskit.circuit.library.U1Gate.reverse_ops")() | For a composite instruction, reverse the order of sub-instructions. |
|
||
| [`to_matrix`](#qiskit.circuit.library.U1Gate.to_matrix "qiskit.circuit.library.U1Gate.to_matrix")() | Return a numpy.array for the U1 gate. |
|
||
| [`validate_parameter`](#qiskit.circuit.library.U1Gate.validate_parameter "qiskit.circuit.library.U1Gate.validate_parameter")(parameter) | Gate parameters should be int, float, or ParameterExpression |
|
||
|
||
## Attributes
|
||
|
||
| | |
|
||
| ---------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------- |
|
||
| [`decompositions`](#qiskit.circuit.library.U1Gate.decompositions "qiskit.circuit.library.U1Gate.decompositions") | Get the decompositions of the instruction from the SessionEquivalenceLibrary. |
|
||
| [`definition`](#qiskit.circuit.library.U1Gate.definition "qiskit.circuit.library.U1Gate.definition") | Return definition in terms of other basic gates. |
|
||
| [`duration`](#qiskit.circuit.library.U1Gate.duration "qiskit.circuit.library.U1Gate.duration") | Get the duration. |
|
||
| [`label`](#qiskit.circuit.library.U1Gate.label "qiskit.circuit.library.U1Gate.label") | Return gate label |
|
||
| [`params`](#qiskit.circuit.library.U1Gate.params "qiskit.circuit.library.U1Gate.params") | return instruction params. |
|
||
| [`unit`](#qiskit.circuit.library.U1Gate.unit "qiskit.circuit.library.U1Gate.unit") | Get the time unit of duration. |
|
||
|
||
### add\_decomposition
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.add_decomposition" signature="add_decomposition(decomposition)">
|
||
Add a decomposition of the instruction to the SessionEquivalenceLibrary.
|
||
</Function>
|
||
|
||
### assemble
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.assemble" signature="assemble()">
|
||
Assemble a QasmQobjInstruction
|
||
|
||
**Return type**
|
||
|
||
`Instruction`
|
||
</Function>
|
||
|
||
### broadcast\_arguments
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.broadcast_arguments" signature="broadcast_arguments(qargs, cargs)">
|
||
Validation and handling of the arguments and its relationship.
|
||
|
||
For example, `cx([q[0],q[1]], q[2])` means `cx(q[0], q[2]); cx(q[1], q[2])`. This method yields the arguments in the right grouping. In the given example:
|
||
|
||
```python
|
||
in: [[q[0],q[1]], q[2]],[]
|
||
outs: [q[0], q[2]], []
|
||
[q[1], q[2]], []
|
||
```
|
||
|
||
The general broadcasting rules are:
|
||
|
||
> * If len(qargs) == 1:
|
||
>
|
||
> ```python
|
||
> [q[0], q[1]] -> [q[0]],[q[1]]
|
||
> ```
|
||
>
|
||
> * If len(qargs) == 2:
|
||
>
|
||
> ```python
|
||
> [[q[0], q[1]], [r[0], r[1]]] -> [q[0], r[0]], [q[1], r[1]]
|
||
> [[q[0]], [r[0], r[1]]] -> [q[0], r[0]], [q[0], r[1]]
|
||
> [[q[0], q[1]], [r[0]]] -> [q[0], r[0]], [q[1], r[0]]
|
||
> ```
|
||
>
|
||
> * If len(qargs) >= 3:
|
||
>
|
||
> ```python
|
||
> [q[0], q[1]], [r[0], r[1]], ...] -> [q[0], r[0], ...], [q[1], r[1], ...]
|
||
> ```
|
||
|
||
**Parameters**
|
||
|
||
* **qargs** (`List`) – List of quantum bit arguments.
|
||
* **cargs** (`List`) – List of classical bit arguments.
|
||
|
||
**Return type**
|
||
|
||
`Tuple`\[`List`, `List`]
|
||
|
||
**Returns**
|
||
|
||
A tuple with single arguments.
|
||
|
||
**Raises**
|
||
|
||
**CircuitError** – If the input is not valid. For example, the number of arguments does not match the gate expectation.
|
||
</Function>
|
||
|
||
### c\_if
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.c_if" signature="c_if(classical, val)">
|
||
Add classical condition on register classical and value val.
|
||
</Function>
|
||
|
||
### control
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.control" signature="control(num_ctrl_qubits=1, label=None, ctrl_state=None)">
|
||
Return a (mutli-)controlled-U1 gate.
|
||
|
||
**Parameters**
|
||
|
||
* **num\_ctrl\_qubits** (*int*) – number of control qubits.
|
||
* **label** (*str or None*) – An optional label for the gate \[Default: None]
|
||
* **ctrl\_state** (*int or str or None*) – control state expressed as integer, string (e.g. ‘110’), or None. If None, use all 1s.
|
||
|
||
**Returns**
|
||
|
||
controlled version of this gate.
|
||
|
||
**Return type**
|
||
|
||
[ControlledGate](qiskit.circuit.ControlledGate "qiskit.circuit.ControlledGate")
|
||
</Function>
|
||
|
||
### copy
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.copy" signature="copy(name=None)">
|
||
Copy of the instruction.
|
||
|
||
**Parameters**
|
||
|
||
**name** (*str*) – name to be given to the copied circuit, if None then the name stays the same.
|
||
|
||
**Returns**
|
||
|
||
**a copy of the current instruction, with the name**
|
||
|
||
updated if it was provided
|
||
|
||
**Return type**
|
||
|
||
[qiskit.circuit.Instruction](qiskit.circuit.Instruction "qiskit.circuit.Instruction")
|
||
</Function>
|
||
|
||
### decompositions
|
||
|
||
<Attribute id="qiskit.circuit.library.U1Gate.decompositions">
|
||
Get the decompositions of the instruction from the SessionEquivalenceLibrary.
|
||
</Attribute>
|
||
|
||
### definition
|
||
|
||
<Attribute id="qiskit.circuit.library.U1Gate.definition">
|
||
Return definition in terms of other basic gates.
|
||
</Attribute>
|
||
|
||
### duration
|
||
|
||
<Attribute id="qiskit.circuit.library.U1Gate.duration">
|
||
Get the duration.
|
||
</Attribute>
|
||
|
||
### inverse
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.inverse" signature="inverse()">
|
||
Return inverted U1 gate ($U1(\lambda){\dagger} = U1(-\lambda)$)
|
||
</Function>
|
||
|
||
### is\_parameterized
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.is_parameterized" signature="is_parameterized()">
|
||
Return True .IFF. instruction is parameterized else False
|
||
</Function>
|
||
|
||
### label
|
||
|
||
<Attribute id="qiskit.circuit.library.U1Gate.label">
|
||
Return gate label
|
||
|
||
**Return type**
|
||
|
||
`str`
|
||
</Attribute>
|
||
|
||
### mirror
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.mirror" signature="mirror()">
|
||
DEPRECATED: use instruction.reverse\_ops().
|
||
|
||
**Returns**
|
||
|
||
**a new instruction with sub-instructions**
|
||
|
||
reversed.
|
||
|
||
**Return type**
|
||
|
||
[qiskit.circuit.Instruction](qiskit.circuit.Instruction "qiskit.circuit.Instruction")
|
||
</Function>
|
||
|
||
### params
|
||
|
||
<Attribute id="qiskit.circuit.library.U1Gate.params">
|
||
return instruction params.
|
||
</Attribute>
|
||
|
||
### power
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.power" signature="power(exponent)">
|
||
Creates a unitary gate as gate^exponent.
|
||
|
||
**Parameters**
|
||
|
||
**exponent** (*float*) – Gate^exponent
|
||
|
||
**Returns**
|
||
|
||
To which to\_matrix is self.to\_matrix^exponent.
|
||
|
||
**Return type**
|
||
|
||
[qiskit.extensions.UnitaryGate](qiskit.extensions.UnitaryGate "qiskit.extensions.UnitaryGate")
|
||
|
||
**Raises**
|
||
|
||
**CircuitError** – If Gate is not unitary
|
||
</Function>
|
||
|
||
### qasm
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.qasm" signature="qasm()">
|
||
Return a default OpenQASM string for the instruction.
|
||
|
||
Derived instructions may override this to print in a different format (e.g. measure q\[0] -> c\[0];).
|
||
</Function>
|
||
|
||
### repeat
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.repeat" signature="repeat(n)">
|
||
Creates an instruction with gate repeated n amount of times.
|
||
|
||
**Parameters**
|
||
|
||
**n** (*int*) – Number of times to repeat the instruction
|
||
|
||
**Returns**
|
||
|
||
Containing the definition.
|
||
|
||
**Return type**
|
||
|
||
[qiskit.circuit.Instruction](qiskit.circuit.Instruction "qiskit.circuit.Instruction")
|
||
|
||
**Raises**
|
||
|
||
**CircuitError** – If n \< 1.
|
||
</Function>
|
||
|
||
### reverse\_ops
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.reverse_ops" signature="reverse_ops()">
|
||
For a composite instruction, reverse the order of sub-instructions.
|
||
|
||
This is done by recursively reversing all sub-instructions. It does not invert any gate.
|
||
|
||
**Returns**
|
||
|
||
**a new instruction with**
|
||
|
||
sub-instructions reversed.
|
||
|
||
**Return type**
|
||
|
||
[qiskit.circuit.Instruction](qiskit.circuit.Instruction "qiskit.circuit.Instruction")
|
||
</Function>
|
||
|
||
### to\_matrix
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.to_matrix" signature="to_matrix()">
|
||
Return a numpy.array for the U1 gate.
|
||
</Function>
|
||
|
||
### unit
|
||
|
||
<Attribute id="qiskit.circuit.library.U1Gate.unit">
|
||
Get the time unit of duration.
|
||
</Attribute>
|
||
|
||
### validate\_parameter
|
||
|
||
<Function id="qiskit.circuit.library.U1Gate.validate_parameter" signature="validate_parameter(parameter)">
|
||
Gate parameters should be int, float, or ParameterExpression
|
||
</Function>
|
||
</Class>
|
||
|