Day 704: Clifford Circuits and Classical Simulation

Learning Objectives

• •**Define stabilizer states** and their representation via stabilizer generators
• •**State the Gottesman-Knill theorem** and its implications for classical simulation
• •**Derive update rules** for Clifford gates acting on stabilizer tableaux
• •**Simulate Pauli measurements** classically using stabilizer formalism
• •**Analyze computational complexity** of stabilizer simulation: $O(n^2)$ per gate, $O(n^3)$ per measurement
• •**Identify limitations** - when does classical simulation fail?

Today's Schedule (7 hours)