Yes. Y² = I. Apply Y twice and you're back to the original state.

Pauli-Y Gate: Interactive Explainer

Q: What's the difference between Pauli-X and Pauli-Y?

Both X and Y flip |0⟩ to |1⟩ and back, but Y also adds a 90° phase. Algebraically Y = i·X·Z.

The Pauli-Y gate

A 180° rotation about the y-axis. Like X, but with an added 90° phase.

Sohum Thakkar · CEO, Qolour

May 8, 2026

The Pauli-Y gate also flips |0⟩ and |1⟩, but adds an extra 90° of phase along the way. On the Bloch sphere, Y is a 180° rotation about the y-axis.

Algebraically, Y = i · X · Z. The i is what makes Y differ from X when acting on a superposition.

Pauli-X: 180° rotation about x (quantum NOT).
Pauli-Z: 180° rotation about z (phase flip).
Hadamard gate: the gate that creates superposition.
What is a quantum gate? The umbrella concept.

Frequently asked questions

What's the difference between Pauli-X and Pauli-Y?

Both X and Y flip |0⟩ ↔ |1⟩, but Y adds a 90° phase along the way. Algebraically: Y = i · X · Z.

Is Y self-inverse?

Yes. Y² = I. Apply Y twice and you're back where you started.