Day 842: T-Gate Fundamentals

Learning Objectives

• •**Define the T-gate** and write its matrix representation
• •**Derive the relationship** between T, S, and Z gates ($T^2 = S$, $T^4 = Z$)
• •**Prove that T is non-Clifford** using conjugation arguments
• •**Explain why T enables universality** when combined with Cliffords
• •**Understand the fault-tolerance challenge** posed by non-Clifford gates
• •**Calculate T-gate action** on various quantum states

Today's Schedule (7 hours)