Day 862: Clifford+T Universality

Learning Objectives

• •**Define the Clifford group** and enumerate its generators {H, S, CNOT}
• •**Explain the Gottesman-Knill theorem** and why Clifford circuits are classically simulable
• •**Prove that adding the T-gate** generates a dense subgroup of SU(2)
• •**Apply the density argument** to show universal approximation capability
• •**Connect Clifford+T to magic state injection** for fault-tolerant implementation
• •**Analyze the structure of Clifford+T circuits** and their computational properties

Today's Schedule (7 hours)