String-Net Model / Toric Code

The toric code (Z₂ string-net model) has qubits on lattice edges. Vertex operators A_v = ∏σˣ enforce closed-loop condition; plaquette operators B_p = ∏σᶻ select equal superposition. Violations create e-anyons (vertex) or m-anyons (plaquette) that come in pairs. Braiding an e around an m acquires a topological phase of -1 (Aharonov-Bohm effect). Click on vertices to place e-anyons, on plaquettes to place m-anyons. Strings connect pairs.