Quantum Network Percolation 2D: Entanglement Swapping Threshold Map

A quantum network only works end-to-end if the nodes along some path can chain enough successful entanglement-swapping events together. This 2D simulator lays out an N×N grid of quantum repeater nodes, 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. A second panel sweeps p_eff across its whole range and plots the averaged giant-cluster fraction, so you can watch the S-curve sharpen into a step as the lattice grows — direct visual evidence of the thermodynamic-limit transition. Drag the lattice to pan, scroll to zoom, tune p, q and N, and resample the random link outcomes by hand or on a repeating timer.