Quantum Network Percolation: Entanglement Swapping Across a Mesh

A quantum network only works end-to-end if the nodes along some path can chain enough successful entanglement-swapping events together. This simulator lays out an N×N grid of quantum repeater nodes on a 2D lattice, generates an elementary entangled pair on each edge with probability p, applies a swap efficiency q at every relay, and asks a single question borrowed straight from percolation theory: does a connected "giant cluster" of usable quantum links span the network from one side to the other? Below the critical density p_eff = p·q = 1/2 the network fragments into small isolated islands; above it, a single giant cluster suddenly spans the whole mesh and any two nodes inside it can be handed long-distance entanglement. Tune p, q and the grid size, resample the random link outcomes by hand or on a repeating timer, and watch the giant cluster appear and disappear right at the threshold.