quantum gate directory
Pauli-Z
Symbol
$Z$
Description:
Phase-flip gate that leaves $|0\rangle$ unchanged and flips the phase of $|1\rangle$.
Alternate notations:
- $Z$
- $\sigma_z$
- $\sigma^z$
- $\sigma_3$
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.ZGate
|
| PennyLane |
pennylane.PauliZ
|
| Cirq |
cirq.Z
|
| Q# | — |
| PyQuil | — |
| Braket | — |
| BQSKit | — |
Groups
This gate is contained in the following groups:
The Pauli-$Z$ gate applies a relative phase of $-1$ to the $|1\rangle$ component.
$$ Z = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} $$
Properties
- Hermitian and self-inverse: $Z^\dagger = Z$ and $Z^2 = I$.
- Equivalent to a $\pi$ rotation about $z$ up to global phase.
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