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Quantum Engineering Year 2: Advanced Quantum Science Month 27Day 745

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Year 2·Month 27·Week 3

Day 745: CSS Code Examples

Day 745 of 2,016~16 min read

Learning Objectives

•**Construct** the Steane code from the Hamming code step-by-step
•**Build** repetition-based CSS codes of any size
•**Design** CSS codes from Reed-Muller codes
•**Compare** different CSS constructions
•**Analyze** encoding circuits for CSS codes
•**Identify** the trade-offs in CSS code design

Today's Schedule (7 hours)

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Overview Schedule Learning Objectives The Steane 713 Code Construction from Hamming Code Verifying Self-Orthogonality Steane Code Stabilizers Logical Operators Codewords Repetition-Based CSS Codes The 311 Bit-Flip Code The 913 Shor Code General Repetition CSS Reed-Muller CSS Codes Reed-Muller Code Review CSS from Reed-Muller Example RM1 3 8 4 4 Example RM1 4 and RM2 4 Punctured Reed-Muller CSS Comparison of CSS Codes Parameter Comparison Rate vs Distance Trade-off Encoding Complexity Encoding Circuits Steane Code Encoding General CSS Encoding Worked Examples Example 1 Verify Steane Code Properties Example 2 Count Steane Codewords Example 3 CSS from BCH Practice Problems Level 1 Direct Application Level 2 Intermediate Level 3 Challenging Computational Lab Summary CSS Code Gallery Key Design Principles Daily Checklist Preview Day 746

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