RX¶
RX rotates a qubit by an angle \( \theta \) about the X-axis of the Bloch sphere - the natural generalization of the Pauli-X gate to any rotation angle.
| Qubits | 1 |
| Parameters | \( \theta \) - rotation angle, in radians |
| Inverse | RX(−θ) |
| Also called | X-rotation |
What it does¶
RX(θ) smoothly interpolates between doing nothing (θ = 0) and a full X gate (θ = π, up to a global phase). Small angles produce a small amount of superposition; π radians fully flips the qubit.
Matrix¶
\[
RX(\theta) = \begin{pmatrix}
\cos(\theta/2) & -i\sin(\theta/2) \\
-i\sin(\theta/2) & \cos(\theta/2)
\end{pmatrix}
\]
Action on basis states¶
- \( |0\rangle \rightarrow \cos(\theta/2)\,|0\rangle - i\sin(\theta/2)\,|1\rangle \)
- \( |1\rangle \rightarrow -i\sin(\theta/2)\,|0\rangle + \cos(\theta/2)\,|1\rangle \)
Example¶
RX with \( \theta = \pi/2 \) on q[0] (starting at \( |0\rangle \)) gives an equal superposition, like H does - but with a different relative phase (an \( -i \) on the \( |1\rangle \) term instead of a plain \( + \)).
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 | rx(theta) q[0]; |
| Qiskit | circuit.rx[theta, q[0]] |
| Cirq | cirq.rx(theta)(q[0]) |
| Q# | Rx(theta, q[0]); |