# CPhaseGate

*class *`qiskit.circuit.library.CPhaseGate(theta, label=None, ctrl_state=None, *, duration=None, unit='dt', _base_label=None)`

Bases: `ControlledGate`

Controlled-Phase gate.

This is a diagonal and symmetric gate that induces a phase on the state of the target qubit, depending on the control state.

Can be applied to a `QuantumCircuit`

with the `cp()`

method.

**Circuit symbol:**

```
q_0: ─■──
│λ
q_1: ─■──
```

**Matrix representation:**

`CRZGate`

: Due to the global phase difference in the matrix definitions of Phase and RZ, CPhase and CRZ are different gates with a relative phase difference.

Create new CPhase 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.

### ctrl_state

Return the control state of the gate as a decimal integer.

### decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

### definition

Return definition in terms of other basic gates. If the gate has open controls, as determined from `ctrl_state`

, the returned definition is conjugated with X without changing the internal `_definition`

.

### 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

Get name of gate. If the gate has open controls the gate name will become:

<original_name_o<ctrl_state>

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.

### num_clbits

Return the number of clbits.

### num_ctrl_qubits

Get number of control qubits.

**Returns**

The number of control qubits for the gate.

**Return type**

### num_qubits

Return the number of qubits.

### params

Get parameters from base_gate.

**Returns**

List of gate parameters.

**Return type**

**Raises**

**CircuitError** – Controlled gate does not define a base gate

### unit

Get the time unit of duration.

## Methods

### control

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

Controlled version of this 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 CPhase gate ($CPhase(\lambda)^{\dagger} = CPhase(-\lambda)$)

### power

`power(exponent, annotated=False)`

Raise this gate to the power of `exponent`

.

Implemented either as a unitary gate (ref. `UnitaryGate`

) or as an annotated operation (ref. `AnnotatedOperation`

). In the case of several standard gates, such as `RXGate`

, when the power of a gate can be expressed in terms of another standard gate that is returned directly.

**Parameters**

**exponent**(*float*(opens in a new tab)) – the power to raise the gate to**annotated**(*bool*(opens in a new tab)) – indicates whether the power gate can be implemented as an annotated operation. In the case of several standard gates, such as`RXGate`

, this argument is ignored when the power of a gate can be expressed in terms of another standard gate.

**Returns**

An operation implementing `gate^exponent`

**Raises**

**CircuitError** – If gate is not unitary