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Quantum Engineering Year 2: Advanced Quantum Science Month 27Day 747

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Year 2·Month 27·Week 3

Day 747: Hypergraph Product Codes

Day 747 of 2,016~13 min read

Learning Objectives

•**Define** the hypergraph product of two classical codes
•**Compute** parameters of hypergraph product codes
•**Understand** how HP codes generalize surface codes
•**Analyze** the LDPC property preservation
•**Compare** HP codes to other CSS constructions
•**Identify** applications in quantum LDPC codes

Today's Schedule (7 hours)

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Overview Schedule Learning Objectives Hypergraph Product Construction Motivation The Hypergraph Product Construction Details Parity Check Matrices Verification of CSS Condition Parameter Analysis Code Dimension Code Distance Rate LDPC Property Examples Example 1 Product of Repetition Codes Example 2 Product with Hamming Code Example 3 Asymmetric Product Connection to Surface Codes Surface Code as Hypergraph Product Beyond Surfaces Quantum LDPC Codes Definition Importance HP Codes as qLDPC Good qLDPC Codes Worked Examples Example 1 Verify HP Parameters Example 2 Construct Parity Check Example 3 Rate Comparison Practice Problems Level 1 Direct Application Level 2 Intermediate Level 3 Challenging Computational Lab Summary Key Formulas Main Takeaways Daily Checklist Preview Day 748

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