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Quantum Engineering Year 2: Advanced Quantum Science Month 26Day 722

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Year 2·Month 26·Week 4

Day 722: Introduction to Code Capacity

Day 722 of 2,016~14 min read

Learning Objectives

•**Review** Shannon's classical channel capacity theorem
•**Define** quantum channel capacity and its variants
•**Explain** the role of capacity in quantum error correction
•**State** the relationship between code rate and capacity
•**Distinguish** between different quantum capacities (Q, C, E)
•**Motivate** the study of capacity for QEC code design

Today's Schedule (7 hours)

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On this page

1 Classical Channel Capacity Review Shannons Channel Coding Theorem The Binary Symmetric Channel BSC 2 Quantum Channels and Capacity Quantum Channel Definition Multiple Quantum Capacities 3 The Quantum Capacity Definition Coherent Information The LSD Theorem 4 Connection to Quantum Error Correction Code Rate and Capacity The Threshold Perspective Example Depolarizing Channel 5 Achievability and Converse Achievability Direct Theorem Converse Strong Converse Finite Block Length Effects 6 Why Capacity Matters for QEC Fundamental Limits Code Design Guidance Comparing Code Families 7 Types of Capacity Problems Code Capacity vs Fault-Tolerant Capacity Independent vs Correlated Errors

Day 721Day 722 of 2,016Day 723