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Quantum Engineering Year 2: Advanced Quantum Science Month 28Day 775

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Year 2·Month 28·Week 3

Day 775: Belief Propagation & LDPC Decoding

Day 775 of 2,016~19 min read

Learning Objectives

•**Construct** factor graphs representing stabilizer code constraints
•**Derive** the sum-product (belief propagation) message update rules
•**Implement** the min-sum algorithm as a practical approximation
•**Analyze** the impact of short cycles on BP performance
•**Apply** BP decoding to quantum LDPC codes
•**Compare** BP thresholds with MWPM and other decoders

Today's Schedule (7 hours)

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1 Factor Graphs for Stabilizer Codes 2 The Sum-Product Algorithm 3 Log-Likelihood Ratio Formulation 4 The Min-Sum Algorithm 5 Convergence and Cycle Issues 6 Quantum LDPC Codes and BP 7 BP-OSD Combining BP with Ordered Statistics

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