Computing Library › Quantum Logic Gates
Quantum Logic Gates
Ry(θ) Rotation Gate
Ry(θ) rotates a qubit about the y-axis by θ — the real-valued rotation that moves amplitude between |0⟩ and |1⟩ without adding a phase.
Matrix
Unitary matrix
cos(θ/2)−sin(θ/2)sin(θ/2)cos(θ/2)
Circuit symbol
Action on basis states
| input | output |
|---|---|
| |0⟩ | cos(θ/2)|0⟩ + sin(θ/2)|1⟩ |
How it works
Ry(θ)=exp(−iθY/2) has purely real entries, so it prepares real superpositions with controllable amplitude — the workhorse of amplitude-encoding and of most variational ansätze.
In code (Qiskit)
python
qc = QuantumCircuit(1)
qc.ry(0.7, 0)single-qubitparametricrotation