The gate zoo
X, Y, Z, phase gates and rotations — every gate is just a rotation of the Bloch sphere.
Pauli gates: X, Y, Z
The X gate is the quantum NOT: it flips |0⟩ ↔ |1⟩, a 180° rotation about the X axis. The Z gate leaves |0⟩ alone but flips the sign of |1⟩'s amplitude — a 180° rotation about the Z axis. Y does both at once.
Z looks like it 'does nothing' if you only watch probabilities — |0⟩ and |1⟩ keep their chances. But the hidden phase it introduces changes how amplitudes interfere later. Sandwich a Z between two H gates and you'll see the difference: HZH acts like an X!
Phase gates: S and T
S and T are gentler versions of Z: they rotate the arrow around the Z axis by 90° and 45° respectively. Two T's make an S; two S's make a Z.
The humble T gate matters enormously in practice: together with H and CNOT it forms a universal set — any quantum computation can be built from just those pieces, the way any digital circuit can be built from NAND gates.
Continuous rotations: Rx, Ry, Rz
The rotation gates take an angle θ and turn the Bloch arrow by exactly that much about the chosen axis. They let you prepare any single-qubit state you like.
In the simulator, click a placed rotation gate to open the angle editor and drag the slider — then watch the Bloch sphere and probability bars move in real time. Ry(θ) applied to |0⟩ gives probability sin²(θ/2) of measuring 1, so the slider is literally a probability dial.
- ◆Every single-qubit gate is a rotation of the Bloch sphere.
- ◆Z, S and T change phases — invisible to immediate measurement but crucial for interference.
- ◆H, T and CNOT together can build any quantum computation.