Kitaev Toric Code & Anyons

The toric code is a 2D quantum error-correcting code built from spin-1/2 qubits on lattice edges. Vertex operators A_v and plaquette operators B_p commute and stabilize the ground state. Exciting pairs of anyons (e-type or m-type) by flipping qubits creates topological excitations that can braid around each other.

e-anyon (A_v= -1)

m-anyon (B_p= -1)

excited qubit (σ_z= -1)

Click on a vertex (intersection) to excite e-anyons, or on a plaquette (cell center) to excite m-anyons. Anyons come in pairs connected by error strings.