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# CPhaseGate¶

class CPhaseGate(theta, label=None, ctrl_state=None)[source]

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:

$\begin{split}CPhase = I \otimes |0\rangle\langle 0| + P \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i\lambda} \end{pmatrix}\end{split}$

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.

Methods Defined Here

 control Controlled version of this gate. inverse Return inverted CPhase gate ($$CPhase(\lambda)^{\dagger} = CPhase(-\lambda)$$) power Raise gate to a power.

Attributes

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 self.ctrl_state, the returned definition is conjugated with X without changing the internal _definition.

duration

Get the duration.

label

Return instruction label

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

int

num_qubits

Return the number of qubits.

params

Get parameters from base_gate.

Returns

List of gate parameters.

Return type

list

Raises

CircuitError -- Controlled gate does not define a base gate

unit

Get the time unit of duration.