quantum gate directory
Pauli-Y
Symbol
$Y$
Description:
Bit-and-phase flip combining $X$ and $Z$ with a phase.
Alternate notations:
- $Y$
- $\sigma_y$
- $\sigma^y$
- $\sigma_2$
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.YGate
|
| PennyLane |
pennylane.PauliY
|
| Cirq |
cirq.Y
|
| Q# | — |
| PyQuil | — |
| Braket | — |
| BQSKit | — |
Groups
This gate is contained in the following groups:
The Pauli-$Y$ gate is a $\pi$ rotation around the $y$ axis of the Bloch sphere.
$$ Y = \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix} $$
Properties
- Hermitian and self-inverse: $Y^\dagger = Y$ and $Y^2 = I$.
- Equivalent to a $\pi$ rotation about $y$ up to global phase.
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