ZGate

class ZGate(label=None)

Bases: qiskit.circuit.gate.Gate

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

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} -1 & 0 \\ 0 & 1 \end{pmatrix} = -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.

Methods Defined Here

ZGate.control(num_ctrl_qubits=1, label=None, ctrl_state=None)

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

ZGate.inverse()

Return inverted Z gate (itself).

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

Return definition in terms of other basic gates.

Get the duration.

Return instruction label

Return type

str

return instruction params.

Get the time unit of duration.

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