Day 564: Rotation Gates (Rx, Ry, Rz)

Learning Objectives

• •**Derive rotation gates** from the exponential map $R_j(\theta) = e^{-i\theta\sigma_j/2}$
• •**Write explicit matrix forms** of Rx(θ), Ry(θ), Rz(θ)
• •**Connect discrete gates** (X, Y, Z, S, T) to specific rotation angles
• •**Apply the Rodrigues formula** for matrix exponentials of Pauli matrices
• •**Compose rotations** using multiplication and understand ordering
• •**Implement continuous gate parameterization** for variational algorithms

Today's Schedule (7 hours)