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

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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: ─■──
q_1: ─■──

Matrix representation:

CPhase=I00+P11=(100001000010000eiλ)CPhase = I \otimes |0\rangle\langle 0| + P \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i\lambda} \end{pmatrix}
See also

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.



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)
>>> type(XGate()) is XGate
>>> XGate().base_class is XGate

In general, you should not rely on the precise class of an instruction; within a given circuit, it is expected that should be a more suitable discriminator in most situations.


The classical condition on the instruction.


Get Clbits in condition.


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


Get the decompositions of the instruction from the SessionEquivalenceLibrary.


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.


Get the duration.


Return instruction label


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.


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


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.


Return the number of clbits.


Get number of control qubits.


The number of control qubits for the gate.

Return type

int(opens in a new tab)


Return the number of qubits.


Get parameters from base_gate.


List of gate parameters.

Return type

list(opens in a new tab)


CircuitError – Controlled gate does not define a base gate


Get the time unit of duration.



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

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Controlled version of this gate.



controlled version of this gate.

Return type




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Return inverted CPhase gate (CPhase(λ)=CPhase(λ)CPhase(\lambda)^{\dagger} = CPhase(-\lambda))


power(exponent, annotated=False)

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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.


  • 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.


An operation implementing gate^exponent


CircuitError – If gate is not unitary

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