Day 703: Symplectic Representation of Clifford Gates

Learning Objectives

• •**Represent Pauli operators** as vectors in $\mathbb{F}_2^{2n}$ (binary field)
• •**Construct the symplectic inner product** and understand its physical meaning
• •**Express Clifford gates** as $2n \times 2n$ symplectic matrices over $\mathbb{F}_2$
• •**Derive symplectic matrices** for H, S, CNOT, and composite gates
• •**Verify symplectic conditions** and compose transformations
• •**Connect symplectic structure** to Pauli commutation relations

Today's Schedule (7 hours)