Topological stabilizer code

A topological stabilizer code is a quantum stabilizer code whose local commuting checks are arranged on a spatial lattice and whose logical information is encoded in global structure. Local errors create detectable syndrome patterns; a nontrivial logical operator typically requires a sufficiently extended chain or surface.

The toric code is a central example: products of Pauli operators around vertices and faces define the stabilizers, while noncontractible loops act on encoded qubits. Protection depends on code distance and an appropriate decoder, not on topology alone guaranteeing error-free storage.