RX Gate (X-Rotation)

RX rotates a qubit around the X axis of the Bloch sphere by any angle you choose. The discrete X gate always flips by exactly 180°. RX generalizes this to a continuous dial. At small angles, it gently tilts the qubit toward the equator. At $\theta =\pi$, it becomes a full X flip. This continuous control is essential for variational quantum algorithms, where you optimize gate angles to find the best solution to a problem.

Partial rotation toward superposition

1. 1Start with $|0⟩$ at the north pole of the Bloch sphere.
2. 2Apply RX$(\pi /2)$. The state becomes ($|0⟩$ − i$|1⟩/\sqrt{2}$. Measurement gives 0 or 1 each with 50% probability.
3. 3The −i factor in front of $|1⟩$ is a phase. It does not affect the 50/50 split, but it matters for later interference.
4. 4Apply RX$(\pi /2)$ again. The two half-rotations compose to a full $\pi$ rotation. The state becomes −i$|1⟩$, which is $|1⟩$ up to global phase.
5. 5Two RX$(\pi /2)$ gates equal one RX$(\pi )$, confirming that RX$(\pi )$ behaves like the X gate.

Parameterized rotations like RX are the backbone of near-term quantum algorithms. VQE and QAOA circuits are built from layers of RX, RY, and RZ gates with angles that a classical optimizer tunes to solve a problem.