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Quantum Engineering Year 2: Advanced Quantum Science Month 29Day 807

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Year 2·Month 29·Week 4

Day 807: Minimum Weight Perfect Matching for Surface Codes

Day 807 of 2,016~18 min read

Learning Objectives

•Construct the syndrome graph from surface code measurements
•Add virtual boundary vertices for planar codes
•Compute edge weights from error probabilities
•Apply the Blossom algorithm for perfect matching
•Handle Y-errors with correlated X and Z syndromes
•Evaluate decoder performance metrics
•Implement a working MWPM decoder

Today's Schedule (7 hours)

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The Decoding Problem Minimum Weight Perfect Matching Syndrome Graph Construction Basic Graph Structure Planar Surface Code Graph Virtual Boundary Vertices Edge Weight Calculation Weight Formula Derivation The Blossom Algorithm Perfect Matching Problem Algorithm Overview Simplified MWPM for Surface Codes Handling Odd Syndrome Count Handling Y-Errors The Y-Error Problem Independent vs Correlated Decoding Correlated Decoding Approaches Weight Adjustment for Y-Errors MWPM Decoder Performance Decoder Metrics Threshold Values Sub-Threshold Scaling

Day 806Day 807 of 2,016Day 808