# ZGate#

class qiskit.circuit.library.ZGate(label=None)[source]#

Bases: Gate

The single-qubit Pauli-Z gate ($$\sigma_z$$).

Can be applied to a QuantumCircuit with the z() method.

Matrix Representation:

$\begin{split}Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\end{split}$

Circuit symbol:

     ┌───┐
q_0: ┤ Z ├
└───┘


Equivalent to a $$\pi$$ radian rotation about the Z axis.

Note

A global phase difference exists between the definitions of $$RZ(\pi)$$ and $$Z$$.

$\begin{split}RZ(\pi) = \begin{pmatrix} -i & 0 \\ 0 & i \end{pmatrix} = -i Z\end{split}$

The gate is equivalent to a phase flip.

$\begin{split}|0\rangle \rightarrow |0\rangle \\ |1\rangle \rightarrow -|1\rangle\end{split}$

Create new Z gate.

Attributes

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

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(num_ctrl_qubits=1, label=None, ctrl_state=None)[source]#

Return a (multi-)controlled-Z gate.

One control returns a CZ 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

inverse()[source]#

Return inverted Z gate (itself).

power(exponent)[source]#

Raise gate to a power.