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Quantum Engineering Year 2: Advanced Quantum Science Month 27Day 732

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Year 2·Month 27·Week 1

Day 732: GF(4) Representation

Day 732 of 2,016~17 min read

Learning Objectives

•**Construct** the finite field GF(4) and its operations
•**Map** single-qubit Paulis to GF(4) elements
•**Use** the trace function to define inner products
•**Convert** between binary and GF(4) representations
•**Understand** additive codes over GF(4)
•**Connect** classical coding theory to stabilizer codes

Today's Schedule (7 hours)

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The Finite Field GF4 GF4 Arithmetic Pauli-to-GF4 Mapping Multi-Qubit Extension Binary to GF4 Conversion The Trace Function Hermitian Inner Product Connection to Symplectic Product Additive Codes over GF4 The CSS Construction in GF4 Weight in GF4 Standard Form for Additive Codes

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