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Quantum Engineering Year 2: Advanced Quantum Science Month 27Day 746

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Year 2·Month 27·Week 3

Day 746: Surface Codes as CSS

Day 746 of 2,016~17 min read

Learning Objectives

•**Construct** the toric code on a periodic lattice
•**Identify** stabilizer generators from vertices and faces
•**Derive** surface code parameters [[n, k, d]]
•**Understand** logical operators as topological cycles
•**Distinguish** toric codes from planar codes
•**Analyze** boundary conditions and their effects

Today's Schedule (7 hours)

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Overview Schedule Learning Objectives The Toric Code Lattice Structure Stabilizer Operators CSS Structure Toric Code Parameters Logical Operators Planar Surface Code Boundary Conditions Standard Surface Code Parameters Logical Operators in Planar Code CSS Interpretation Classical Codes for Surface Code Chain Complex Perspective Homological Quantum Codes Toric Code Detailed Analysis Small Example 22 Toric Code Error Detection and Correction Surface Code Distance Minimum Weight Logical Operators Error Threshold Rotated Surface Code Improved Layout Example d3 Rotated Code Worked Examples Example 1 Count Toric Code Parameters Example 2 Verify CSS Commutation Example 3 Find Logical Operators Practice Problems Level 1 Direct Application Level 2 Intermediate Level 3 Challenging Computational Lab Summary Key Formulas Main Takeaways Daily Checklist Preview Day 747

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