Day 706: Normalizer Structure and Clifford Circuit Synthesis

Learning Objectives

• •**Characterize the Clifford group** as the normalizer of the Pauli group
• •**Decompose Cliffords** as a semidirect product $\mathcal{C}_n = \mathcal{P}_n \rtimes Sp(2n, \mathbb{F}_2)$
• •**Compute minimal generating sets** for the Clifford group
• •**Apply the Bruhat decomposition** to Clifford unitaries
• •**Synthesize efficient Clifford circuits** from tableaux
• •**Optimize Clifford circuits** via gate cancellation and reordering

Today's Schedule (7 hours)