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Quantum Engineering Year 2: Advanced Quantum Science Month 28Day 772

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Year 2·Month 28·Week 3

Day 772: Minimum Weight Perfect Matching (MWPM)

Day 772 of 2,016~19 min read

Learning Objectives

•**Construct** the syndrome graph from surface code defect positions
•**Explain** the mapping from decoding to minimum weight perfect matching
•**Describe** the Blossom algorithm for polynomial-time matching
•**Implement** MWPM decoding for rotated surface codes
•**Analyze** the $O(n^3)$ complexity and threshold performance
•**Handle** weighted edges for correlated and spatially-varying noise

Today's Schedule (7 hours)

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On this page

1 From Syndromes to Graphs 2 The Perfect Matching Problem 3 The Blossom Algorithm 4 Weighted Matching for Realistic Noise 5 Boundary Handling 6 Measurement Errors and Space-Time Decoding

Day 771Day 772 of 2,016Day 773