Single-Qubit

Rotation Y (RY)

Rotates the qubit state by angle θ around the Y-axis of the Bloch sphere.

Mathematical Representation
cos(θ/2)
-sin(θ/2)
sin(θ/2)
cos(θ/2)
Syntax & Usage Examples
RY 0
RY 0 0.5
RY(1) 0
RY (0,1)
RY [0,1] 90deg
RY(1rad) 0
Bloch Sphere Representation
|0⟩ |1⟩ |+⟩ |−⟩ |−i⟩ |i⟩
θ rotation about the Y-axis
Qubi Gate Block Definition

This is how the RY gate is defined in Qubi preprocessor style. You can declare similar definitions in custom gate { } blocks:

gate RY {
  name: Rotation Y
  label: RY
  color: #16a34a
  matrix: [cos(θ/2) -sin(θ/2); sin(θ/2) cos(θ/2)]
  qubits: 1
}
Circuit Builder Layout
q[0]RY

Technical Reference Details

Default angle is π/2 when omitted. Use RY(θ) q for inline angles (attached parentheses). RY (0,1) applies the same rotation to qubits 0 and 1 in parallel. RY(π) is equivalent to Y up to global phase.

Parameter: θ (default: π/2)
LaTeX formula: \begin{bmatrix}\cos(\theta/2)&-\sin(\theta/2)\\\sin(\theta/2)&\cos(\theta/2)\end{bmatrix}
Compiler Representation: Gate ID is RY.
Try RY in Simulator