Day 829: Union-Find Decoder

Learning Objectives

• •**Explain** the Union-Find data structure and its near-constant-time operations
• •**Describe** the cluster growth algorithm for syndrome decoding
• •**Implement** a complete Union-Find decoder for surface codes
• •**Analyze** the time complexity $O(n \cdot \alpha(n))$ and its practical implications
• •**Compare** Union-Find threshold (~9.9%) to MWPM threshold (~10.3%)
• •**Evaluate** the accuracy-speed trade-off in real-time decoding scenarios

Today's Schedule (7 hours)