Day 773: Union-Find Decoders

Learning Objectives

• •**Implement** the Union-Find data structure with path compression and union by rank
• •**Explain** the cluster growth algorithm for topological code decoding
• •**Derive** the almost-linear $O(n \cdot \alpha(n))$ time complexity
• •**Analyze** the inverse Ackermann function and why it's effectively constant
• •**Compare** Union-Find threshold (~9.9%) against MWPM (~10.3%)
• •**Implement** the peeling decoder variant for erasure channels

Today's Schedule (7 hours)