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

decompositions¶: Get the decompositions of the instruction from the SessionEquivalenceLibrary.