Quantum Self-Correcting Stabilizer Codes

In this paper, we explicitly construct (Abelian) anyonic excitations of arbitrary stabilizer Hamiltonians which are local on a 2D lattice of qubits. This leads directly to the conclusion that, in the presence of local thermal noise, such systems cannot be used for the fault-tolerant storage of quantum information by self-correction i.e. they are ruled out as candidates for a `quantum hard drive'. We suggest that in 3D, the same construction leads to an argument that self-correction is impossible.