Computing Library › Quantum Logic Gates
Quantum Logic Gates
Rx(θ) Rotation Gate
Rx(θ) rotates a qubit by an arbitrary angle θ about the x-axis — a continuous, parametric bit-axis rotation.
Matrix
Unitary matrix
cos(θ/2)−i·sin(θ/2)−i·sin(θ/2)cos(θ/2)
Circuit symbol
Action on basis states
| input | output |
|---|---|
| |0⟩ | cos(θ/2)|0⟩ − i·sin(θ/2)|1⟩ |
How it works
Rx(θ)=exp(−iθX/2). At θ=π it is X (up to global phase). Parametric rotations Rx/Ry/Rz are the tunable knobs of variational circuits (VQE, QAOA) and of pulse-level calibration on real hardware.
In code (Qiskit)
python
from numpy import pi
qc = QuantumCircuit(1)
qc.rx(pi/2, 0)single-qubitparametricrotation