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Quantum Engineering Year 2: Advanced Quantum Science Month 27Day 751

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Year 2·Month 27·Week 4

Day 751: Reed-Muller Quantum Codes

Day 751 of 2,016~12 min read

Learning Objectives

•**Construct** classical Reed-Muller codes RM(r, m)
•**Compute** RM code parameters and dual relationships
•**Build** quantum codes from Reed-Muller codes
•**Explain** why certain RM codes have transversal T gates
•**Apply** RM codes to magic state distillation
•**Compare** RM codes with other CSS constructions

Today's Schedule (7 hours)

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Overview Schedule Learning Objectives Classical Reed-Muller Codes Definition Generator Matrix Construction Dual Code Relationship Self-Orthogonality Quantum Reed-Muller Codes CSS Construction Example 8 0 4 from RM1 3 The 15 1 3 Reed-Muller Code Transversal T Gate The Remarkable Property Why T is Transversal Doubly-Even Property Magic State Distillation T States 15-to-1 Distillation Connection to RM Codes Code Comparison RM-Based Quantum Codes Steane vs 15-qubit RM Worked Examples Example 1 Compute RM Parameters Example 2 Verify Dual Relationship Example 3 CSS from RM Codes Practice Problems Level 1 Direct Application Level 2 Intermediate Level 3 Challenging Computational Lab Summary Key Formulas Main Takeaways Daily Checklist Preview Day 752

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