Type-I and Type-II Fusion Protocols for Weighted Graph States
The analysis examines how Type-I and Type-II fusion operations affect weighted graph states used for measurement-based quantum computation (MBQC). It finds that Type-I fusion is robust, acting exactly like the unweighted case by preserving weights. However, Type-II fusion is limited because creating a logical qubit depends on specific weight configurations, and its failures destroy the desired graph structure unless specific conditions are met.