Day 565: Bloch Sphere Representation

Learning Objectives

• •**Prove any U ∈ SU(2)** can be written as $U = e^{i\alpha}R_{\hat{n}}(\theta)$
• •**Extract axis and angle** from a given unitary matrix
• •**Understand the SU(2) manifold** structure and its topology
• •**Convert between parameterizations** (matrix, axis-angle, Euler angles)
• •**Visualize gate actions** geometrically on the Bloch sphere
• •**Apply the double-cover relationship** between SU(2) and SO(3)

Today's Schedule (7 hours)