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# ZGate¶

class ZGate(label=None)[Quellcode]

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.

Bemerkung

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.

Methods Defined Here

 control Return a (multi-)controlled-Z gate. inverse Return inverted Z gate (itself). power Raise gate to a power.

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.