Day 955: HHL Algorithm Derivation

Learning Objectives

• •**Derive the complete HHL algorithm** step by step from first principles
• •**Explain the eigenvalue inversion mechanism** via controlled rotation
• •**Analyze the success probability** and role of amplitude amplification
• •**Calculate the complexity** $O(\log(N) \cdot s^2 \cdot \kappa^2 / \epsilon)$
• •**Compare HHL to classical algorithms** quantifying the exponential speedup
• •**Identify the key assumptions** required for quantum advantage

Today's Schedule (7 hours)