Computing Library › Quantum Logic Gates
Quantum Logic Gates
Rz(θ) Rotation Gate
Rz(θ) rotates a qubit about the z-axis — a pure phase between |0⟩ and |1⟩, often free or nearly free on hardware.
Matrix
Unitary matrix
e^{−iθ/2}00e^{iθ/2}
Circuit symbol
Action on basis states
| input | output |
|---|---|
| |0⟩ | e^{−iθ/2}|0⟩ |
| |1⟩ | e^{iθ/2}|1⟩ |
How it works
Rz(θ)=exp(−iθZ/2). On many platforms z-rotations are 'virtual' — implemented by shifting the phase reference of later pulses — so they cost no time and no error, making Rz the cheapest parametric gate.
In code (Qiskit)
python
qc = QuantumCircuit(1)
qc.rz(0.5, 0)single-qubitparametricrotationvirtual