# U1Gate

`qiskit.circuit.library.U1Gate(theta, label=None, *, duration=None, unit='dt')`

GitHub(opens in a new tab)

Bases: `Gate`

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).

This gate is deprecated. Instead, the following replacements should be used

$U1(\lambda) = P(\lambda)= U(0,0,\lambda)$```
circuit = QuantumCircuit(1)
circuit.p(lambda, 0) # or circuit.u(0, 0, lambda)
```

**Circuit symbol:**

```
┌───────┐
q_0: ┤ U1(λ) ├
└───────┘
```

**Matrix Representation:**

**Examples:**

$U1(\lambda = \pi) = Z$ $U1(\lambda = \pi/2) = S$ $U1(\lambda = \pi/4) = T$

`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(opens in a new tab)

Create new U1 gate.

## Attributes

### base_class

Get the base class of this instruction. This is guaranteed to be in the inheritance tree of `self`

.

The “base class” of an instruction is the lowest class in its inheritance tree that the object should be considered entirely compatible with for _all_ circuit applications. This typically means that the subclass is defined purely to offer some sort of programmer convenience over the base class, and the base class is the “true” class for a behavioural perspective. In particular, you should *not* override `base_class`

if you are defining a custom version of an instruction that will be implemented differently by hardware, such as an alternative measurement strategy, or a version of a parametrised gate with a particular set of parameters for the purposes of distinguishing it in a `Target`

from the full parametrised gate.

This is often exactly equivalent to `type(obj)`

, except in the case of singleton instances of standard-library instructions. These singleton instances are special subclasses of their base class, and this property will return that base. For example:

```
>>> isinstance(XGate(), XGate)
True
>>> type(XGate()) is XGate
False
>>> XGate().base_class is XGate
True
```

In general, you should not rely on the precise class of an instruction; within a given circuit, it is expected that `Instruction.name`

should be a more suitable discriminator in most situations.

### condition

The classical condition on the instruction.

### condition_bits

Get Clbits in condition.

### decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

### definition

Return definition in terms of other basic gates.

### duration

Get the duration.

### label

Return instruction label

### mutable

Is this instance is a mutable unique instance or not.

If this attribute is `False`

the gate instance is a shared singleton and is not mutable.

### name

Return the name.

### num_clbits

Return the number of clbits.

### num_qubits

Return the number of qubits.

### params

return instruction params.

### unit

Get the time unit of duration.

## Methods

### control

`control(num_ctrl_qubits=1, label=None, ctrl_state=None, annotated=False)`

Return a (multi-)controlled-U1 gate.

**Parameters**

**num_ctrl_qubits**(*int*(opens in a new tab)) – number of control qubits.**label**(*str*(opens in a new tab)*| None*) – An optional label for the gate [Default:`None`

]**ctrl_state**(*str*(opens in a new tab)*|**int*(opens in a new tab)*| None*) – control state expressed as integer, string (e.g.``’110’`), or ``None`

. If`None`

, use all 1s.**annotated**(*bool*(opens in a new tab)) – indicates whether the controlled gate can be implemented as an annotated gate.

**Returns**

controlled version of this gate.

**Return type**

### inverse

`inverse(annotated=False)`

Return inverted U1 gate ($U1(\lambda)^{\dagger} = U1(-\lambda))$

**Parameters**

**annotated** (*bool*(opens in a new tab)) – when set to `True`

, this is typically used to return an `AnnotatedOperation`

with an inverse modifier set instead of a concrete `Gate`

. However, for this class this argument is ignored as the inverse of this gate is always a `U1Gate`

with inverse parameter values.

**Returns**

inverse gate.

**Return type**