Pauli-Y¶
The Pauli-Y gate flips the qubit like X, but also rotates its phase - it's the "bit-and-phase-flip" member of the Pauli family.
| Qubits | 1 |
| Parameters | None |
| Inverse | Itself (Y² = I) |
| Also called | Y gate |
What it does¶
Y swaps \( |0\rangle \) and \( |1\rangle \) like X does, but multiplies each resulting amplitude by \( \pm i \). It is equal, up to a global phase, to applying Z and then X (or X then Z, with opposite sign): \( Y = iXZ \).
Matrix¶
Action on basis states¶
- \( |0\rangle \rightarrow i\,|1\rangle \)
- \( |1\rangle \rightarrow -i\,|0\rangle \)
Phase and Bloch-sphere effect¶
On the Bloch sphere, Y is a 180° rotation about the Y-axis - it swaps the poles like X, but rotates points on the equator in the opposite sense to X.
Example¶
Placing Y on q[0] (initially \( |0\rangle \)) prepares \( i\,|1\rangle \). In the Statevector panel, the 1 amplitude has the same magnitude as an X gate would give, but a different phase color.
Other notations¶
Naming conventions across ecosystems; exact syntax can vary by library version, and this does not claim to be Qompile's generated output unless otherwise noted.
| Language | Typical form |
|---|---|
| OpenQASM 2.0 | y q[0]; |
| Qiskit | circuit.y[q[0]] |
| Cirq | cirq.Y(q[0]) |
| Q# | Y(q[0]); |