Toric Code — Topological Error Protection

Kitaev's toric code encodes qubits in the ground state of a lattice Hamiltonian. Errors (bit flips on edges) create pairs of "anyonic" excitations at vertices (A-type) and plaquettes (B-type). The code is protected because correcting errors requires finding minimal-weight matchings.

Syndrome: 0 vertex violations, 0 plaquette violations